Is it acceptable to retrofit a new-work plastic electrical box by screwing through it into a stud?
Yes, as redlude97 mentions, they make boxes designed to mount this way.  They're often sold as old/new work boxes since they can be used just as easily either way.
Here's a picture of a typical example.  This one is made by Arlington and sold by Platt, (though this is not an endorsement of either of those companies; it just happened to be the first google result):

Edit in response to your question edit:
Since you're asking specifically about using a new work box not designed for this purpose, that would most likely not be allowable unless the manufacturer specifically allows it in their instructions.  One of the primary jobs of electrical boxes is keeping contained any fires that may try to start inside of them, and UL (or other testing labs) make sure they do -- provided they're unmodified.  Once you start adding holes in them that the manufacturer didn't put there, then they can no longer guarantee their fire performance, and their UL listing is technically no longer valid.  Now, an inspector might not notice, and just assumed you used one of the ones designed to be mounted this way, but it would still be a code violation.  This falls under Sec. 110.3(B) of the electrical code -- you must follow manufacturers instructions when installing listed equiptment.