Dagmar
Defender of the Bunnies of Skyrim
Some will respawn, some wont, but it has nothing to do with them being at the College or the Arch-mages Quarters. The Arch-mages Quarters is not a safe location (which is why the garden regrows if the place is not visited for 30 days)The containers in archmages quarters and the college room you get don't respawn.
The furniture containers, ie. cupboards, dressers, end tables, wardrobes and strongbox will not respawn because those containers are not coded to respawn wherever they are found in Skyrim. Everything else at the College of Winterhold (barrels, sacks, satchels) will eventually respawn their contents.