Short term? Terribly. Long term? With any luck you'll develop standards and methods like you have for other aspects of the job and you'll have a tighter set of CDs. The idea of consultant spec writers has always pissed me off. It's literally the MOST IMPORTANT PART OF THE CDS.

Frankly I'm surprised that any spec writers stick it out for longer than a few months at any firms.  Mostly what I've seen is that any firm large enough to have their own spec writer(s) have many many ongoing projects, each with teams of design and management staff - anywhere from 3 to 20 people working on the drawing set for any given project - and one spec writer handling 4, 6, 8, 20 projects, with, at best, an administrative assistant or receptionist doing a little typing assistance.  For a drawing set with a few hundred sheets the project manual can easily have 1000+ pages, with one person to coordinate all of it.  And when the design and production team finally hits its deadline and collapses in a heap for three days afterward, the spec writer is right onto the next project and might have another three deadlines in those three days, and they're supposed to not only know everything about every product and construction, but everything about every project they're working on.

The same people who pride themselves on running out a red pen marking up a drawing set will avoid delving into the specs as if the project manual will give them leprosy - and yet the spec writer gets all the grief when there's a change order for anything spec-related.

In my opinion everybody should have to put together a project manual at least once, just to get permission to start the license exam.

If the PA's work together and devote some time to generating some good spec writing practices, you may be ok.   Look at investing in some structured training on spec writing or form a study group.  It will certainly make the individual PA's skill set stronger and more well rounded.  

You really need to have good specs if you are doing government work that has to be bid publicly. 

In the long run it might be a good idea, but unless the firm specializes in a particular building type it's going to be a bumpy transition.  A lot of folks inexperienced in specifications learning on the job with the employer taking on the legal exposure.  Great for their professional development, but if I was the boss I'd be very nervous.  Who is going to do the PA's work while they are taking on this additional burden?  Are they adding staff for that?

On a random project a PA was really eager to do some spec writing themselves. I said go for it! Took them 3 days plus entire weekend to write a single spec. It was a pretty complex spec, but still. Decent way to allocate time for specification services is one hour per spec (and then it gets less than that for multiple passes), and some specs can be put together in 5 minutes and others may take half day. 

Any experienced architect should theoretically be able to write specs. The issue is being efficient at it. Dedicated spec writer will also have a much larger palette to draw from. What may be a completely new product or system to any PA, I've specified it dozens of times before. 

Inexperienced people are likely to copy specs or parts of them from past projects without necessarily understanding what they're "writing", and add things that sound good to them, without always understanding whether they're creating conflicts or increasing the likelihood of change orders.  It's fine to let them do it, how else are they going to learn after all, but there will need to be a schedule in place that allows extensive review and corrections, and someone or someones available and with the skills to do that extensive review.  If your spec writers have already left, who is going to do that?  You might want to hire a consultant spec writer on the first few of these projects, not to write the specs but to review and give recommendations on the specs that the folks in your firm write.

We do use masterspec.  The above makes me feel better about the whole thing.  I'm mostly worried about how much time it will take to do something I've never done before, with no one to review it

Most of the senior arch staff do their own abridged specs directly on CDs on smaller projects. For the large ones, there are 3 people (2 arch and one tech, all equity partners) who will produce the 800 page book. We constantly have issues and I’ve been made to look like a fool on site or in client meetings more than once. I’m actually pretty tired of apologizing due to a spec hole or circular reference.