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The documentation is pretty vague about why it won't work. It just says it will yield unexpected results and Adobe will not support deviating from the implementation instructions.
In truth, I have not really spent a whole lot of time investigating what actually breaks, what can and cannot be done when outputting the DTM tags through another tag manager or otherwise dynamically appending it to the page. Because for me, the answer is simple: don't do it. Adobe's tools (Target, Audience Manager, Analytics, etc. ) are enterprise level tools with enterprise level prices attached to them, so making sure I implement them in a way that is supported by Adobe seems like a no-brainer, even if it means sticking within the confines of its limitations. If my clients lose data because something went wrong, that usually equates to thousands, sometimes millions of dollars lost. I certainly don't want to be the guy the finger gets pointed at. Especially if it's because of something I willfully did, like deviate from the instructions!
In any case, even having said all that.. there is no solid answer for "Will this work?", because the answer to that largely depends on everything you have implemented through DTM, which is unique to you. But in general, I think for sure the biggest issues are with timing. So, if you do not have anything implemented in DTM on a Tool level, and if you only have 3rd party tags implemented in page load rules configured to be output on DOM Ready or Window Load, and have them configured to be appended async, then in practice you will probably be okay outputting DTM through GTM.
But overall, all I can really say is give it a try. Add your DTM tag to GTM and thoroughly test everything you have deployed through DTM, and check to make sure everything looks good and works as expected. But again (and I'm sorry for beating a dead horse here), understand that even if everything looks shiny to you, you're still on your own for support if things start looking shady down the line :/