By no means impossible. In "AGT", the future timeline makes no references to the past that would contradict the events of ST:GEN, and we can assume that the past timelines of "AGT" are not relevant to the discussion. Things could indeed proceed in a sequence that involves both ST:GEN and the future part of "AGT".
In a vague sense, that's what a Galaxy-class saucer section is to begin with: a fully functional ship bolted onto the stardrive section.
The jury is still at each other's throats over whether the saucer had proper warp drive aboard. That would IMHO be the deciding point: bolting together two ships of roughly similar size (that is, not merely a mothership and a warpshuttle) that both are independently capable of interstellar travel sounds wasteful and nonproductive.
The combination of a powerful tug and an assortment of mission spacecraft towed by her is sensible enough, assuming that it is not easy to pack the gear for multiple missions in a single hull. A Galaxy
-like ship with two or three saucers could well be a logical construct, too: all three could be combat saucers in wartime, but only one in peacetime, the other two then catering for exploration and colony logistics or whatever. Once this setup is modified so that the tug actually drops off a mission spacecraft somewhere and later comes to pick her up, though, things get a bit overcomplicated and inflexible again: the mission spacecraft might then be better off having her very own warp engines.