Run away and don't look back.

I wouldn't worry too much about experience; the learning curve is quick on site.  Depending on the type and scale you might work in, it can range from very hands or feeling very administrative in a larger project/company.  The latter will deal a lot with submittals, RFIs, procurement of materials and labor, coordination, etc.  These are useful experiences that could help inform good design practice later, but it can be soul crushing work to some.  So, ask lots of questions, especially about work/life balance, day to day activities, bonuses, time off, etc.  CMs make good money and get good benefits because some work many hours during pinch points in a job. 

Also, if you do value designing, ask yourself if you are willing to have only a competition here or there to stay fresh.  But realize that design thinking can really help solve problems and can be rewarding while on that side of the fence.  Best of luck.

Personally, it seems that it would be more handy to have experience in entry level CM than having experience in entry level architecture since most arch. entry level jobs consist of the typical red line pick ups and CAD drafting. I'd also imagine it would be easier to transition back to architecture from CM than the other way around.

I thought about this alternate path a lot during my studies and if I could go back in time, I would have definitely chosen the CM positions over architecture instead. My experience as a recent M Arch grad is that the entry level arch graduate / intern jobs are not that much more different than school (I came from a tech background for undergrad). The only difference is that you have gone through the M Arch or B Arch schooling but lack the relevant practical skills. Other than that, most entry level arch jobs are no more than just glorified 'draft monkeys' for the firm. My experience in the field is that practical experience is valued much more for majority of job opportunities and having practical experience on the in's and out's of construction and building is much more beneficial to a firm than just drafting skills alone. Drafting is easy and can be taught/trained but experience has to be earned. Just my two cents...

You can learn a hell of a lot in a CM or Owner's Rep position.

I did about 18 months of intensive CAD monkeying and then moved into being an Owner's rep with heavy exposure to CA and CM.   It was like going to graduate school.   Interacting with multiple architecture firms exposed me to a diverse range of different ways people did and drew things.

Do the CM job for a year or however long duration can be used for AXP.  Most entry level architecture jobs suck.  You will not be missing much.

Just don't let your design and drafting skills atrophy.

What type of renovations, sf, and $$ value of projects will you be working on? Residential, commercial, educational? <50,000sf, 250,000+sf? $1m, $100m? That may impact the breath and depth of knowledge you gain. 

At my company the assistant PMs are put in charge of different "packages" (ex. fire protection, electrical, millwork, plumbing, etc). On a smaller job you'll likely manage more packages than on a larger job, meaning the knowledge you gain directly working with a trade may be limited to the trades in the packages you manage. You will learn a lot, especially if you're a visual or hands on learner.

I'd imagine if you try to transition back later you would be able to in a construction administration role. You'll likely be much better prepared for it than others your age because you'll have seen everything that can go wrong in the field and know how the fix it, or better yet avoid it in the first place. A design role would be more difficult to get. For what it's worth I enjoyed doing design coming out of school. Most of us do, but not everyone gets to design, and it's different when you have clients, budgets, other stakeholders, etc. 

Last thing. If you're doing renovation work on larger projects, I hope your company uses laser scanning equipment if it's not cost-prohibitive. Measuring everything with a tape and disto-meter is incredibly inefficient and prone to error. 

I can relate here. I graduated last year with an M.Arch. I had some internship experience at an Arch firm while in school, but then got a job as an assist. PE during my last year. I worked on a historic $15mil, 30k sf multifamily remodel where the developer and the GC were one and the same. I really enjoyed the work. Stressful, especially in congruence with my thesis, but loved being in the construction realm. Had to interface with all sorts of positions from construction trades to investors which I think was useful. It was an atypical position with the GC and developer being the same company, but I got to work closely with the architects which felt like more of a design role. I didn't expect to like the construction side as much as I did, but I decided to pursue that track further. 

Now I work for a different GC that also develops some of their own projects, they are a smaller outfit however. Most of the projects I do now are single family residential both new construction and remodels. The people that I work with are much more pleasant and the work/life balance is more my pace now. For me, I'm finding justification in the scope of work and doing what I am interested in, having the work/life balance after coming out of school. I've been told repeatedly by architects that the track I'm pursuing will be valuable, but I also worry about the holes in my Arch progress, especially in reference to all my peers who are doing a more traditional route. I think I still feel like I am learning new and valuable things every day, and when that stops will be when I reconsider.