I did this for awhile.

Biggest issues:
1. at some points there was more on my plate than I could deal with, at others I couldn't drum up enough work to survive. Remember that if you're an itinerant intern you're still dealing with the schedules of the firms that might want to utilize you. In other words, it's not quite the same as working for yourself, where you'd have a certain ability to juggle projects and deadlines and create a backlog of work that will allow you a steady income and where you can save up some of that work to carry you over leaner times.
There's no way to "save up" projects in the scenario you're describing. You're still for the most part at the mercy of the existing project deadlines.

2. Taxes. Since you'll be working as an independent contractor you'll be paying twice as much in social security as you are now.
Also, if you live in a municipality that taxes businesses on their assets then every year you'll be paying them part of the worth of your office - everything from your computer to your chair if you work from home. In some cities it doesn't matter whether or not you've registered/incorporated/any other way made the existence of your business "official" - as soon as a 1099 is generated for you from one of these employers, they'll consider your "business" fair game.

Part of the reason these firms you're considering can't hire another person right now is because of the costs of their share of payroll taxes and employee benefits. The reason it is appealing to them to hire you as an independent contractor is exactly because you'd be shouldering all those costs yourself.

3. Eventually I did decide I wanted to finish IDP and take the ARE. All of the time that I was self-employed did not count toward that. Keep this in mind in your ultimate career timeline/goals. Unless you're working under the direct supervision of a registered architect, on their premises, for a minimum of 35 hours per week for 10 weeks straight (or min 20 hours per week for 6 months straight) then you can't count whatever you're doing toward minimum IDP units.

I have done some freelance work at various times, and basically I think it's only worth it if you have a specific reason why you want to be working part time. For the above mentioned reasons, unless they are really paying you a LOT more than you would be making at a full-time job, it becomes a pain and not worth it emotionally or financially. You end up working all the time but not making ends meet.
On the other hand, if you have some side projects of your own and are looking to supplement your income, or have been laid off and aren't ready to jump back in to the fullt-ime world (both situations I've been in), it makes sense. I do know a few people who prefer to work freelance because of their personality (like to sleep late, work late) or legal situation(no visa), but they generally work for friends.

I did a lot of this back when I was starting out and the big issue I always ran into from most small firms was that they would not pay me until their client paid them, even if my contract with them called for payment upon completed phases. They tended to agree up front then hold payment when the time came, citing the client non-payment thing. I have held onto many CAD files until I was paid and while it may have burned a few bridges, there were many jobs I did before where the client never got construction financing, the project died so the architect never got paid then neither did I.

Watch yourself and don't be afraid to be VERY specific on transfer of files and payment terms in your agreement with the architect. Phased payments helped a lot to keep from being burned on too much of my time should a project go south.

Unlike RA Rudolph, I found it to be very worth it for me, financially and expanding my experience that was role-limited at my day job early on. And as I did most projects on a fixed fee rather than hourly, I was pushed into developing my own methodology for maximum effeciency of producing fast CD's in the early days of ACAD. It pushed me into becoming the XREF guru, which was not used by many others at all at the time.

Hmm, interesting, I would NEVER agree to do anything for a fixed fee, and I've never had problems getting paid either - to each his own. I wasn't trying to say it's not worth it, just not worth it for everyone...

It depends on what you are doing, but I like fixed fees. If you are working at your own place, get 25-50% of the fees up front. Any client that is honest shouldn't have a problem with that. This gives you money in hand, so you can plan.
Hourly can be great, as long as you know you are going to get it for a certain amount of time. It'd suck if you were planning on, say, $500 a week (not for full time, of course) from somewhere and they didn't let you work your hours, it'd screw your planning and potential to get other jobs. This happened to me and it sucked. I had made plans accordingly to accommodate them, and they kept pushing it back (hey, can you come in tomorrow instead? type of things).

If you do work in other offices, make sure you get in writing how and when you'll be paid. I would never agree to be paid when they get paid, that's just bad business.

Don't mess around if you still need IDP credits.

well.... I'll put in my two cents since I freelance and deal with clients, not firms. I started freelancing when I got out of Architecture school(B.A. in Arch). A friend asked if I would help him remodel his home, since I now had a degree and I agreed.... from that project the freelancing took off... however, I was doing it only as a side job to supplement my income from a full-time job that had nothing to do with Architecture.... now that I don't have that full time job (budget cuts in government) I can tell you that it by no means matches to what I was making before, and now that I have more jobs, it sometimes gets real dicey with clients and the city planners/plan checkers. I like doing it, but it can really be stressful, and like someone else mentioned sometimes the money pours and sometimes it doesn't. I enjoy the experience that I'm getting learning all phases of how a project gets built,dealing with clients, government's, and learning strutural details and materials. I set my own hours, work on projects in my house, and can "call in sick" or take a vacation whenever I want. Looking at friends working for firms, I think the above mentioned is the only advantage of freelancing, than working for a firm doing redlines all day. I get to see and be involved in the full scope of things. I do however want and need to get licensed, so with that said... your situation sounds good because you are not dealing with just contractors and regular joe's that can't provide any credits towards IDP. You will also maybe get to work on non-Residential projects which is what us 'Designers' are pretty much limited to. Plus, I imagine the firms will be signing the projects, so it eliminates costs to have work stamped by an Engineer when required by the city, this equals 0 liability, which will let you rest a little easier, and with more money in your pockets. Good luck on your decision.