Yes they can. I did exactly this as prep for summerset, crafted ~40 items, went to Rolis and did nothing but accept/turn in. It only works if you craft them with the char turning in, though, so no crafting for alts.
Alchemy and food works for any char, but you have to craft once on top of the stack in order to make it count all.
If you're on PC, the above add-on is a godsend - it gives you the ability to right-click the sealed writ, select the option 'craft writ' and next time you're at the appropriate craft station, it'll craft exactly that. Only things it doesn't work with are alchemy writs.
PC/NA: Primarily Daggerfall Covenant.
Lennie: Breton Sorceror. 9-trait crafter on everything, purveyor of useless frippery.