If I recall correctly Bill Belichick pioneered the roster management philosophy of retaining two, rather than three quarterbacks on the 53-man roster.
Unique circumstances in 2016 caused a deviation from that thought process, with three quarterbacks.
If Garoppolo is traded I would expect the Patriots to return to a two QB setup. A third quarterback will definitely be signed for training camp (in part for injury insurance, and in part to limit the number of throws Brady has to make over the course of seven months).
A rookie might be drafted late or signed as a free agent, potentially landing on the prayctice squad. But a veteran like Hoyer would be nothing more than camp fodder and kept on the top of the shadow roster list.