Can I use sleeve protectors for Dominion cards and still fit them back into the box?
I use the Mayday games sleeves for all my Dominion cards.

The sets of 10 Kingdom cards will still fit in their slots in the box just fine.  More numerous cards (like the Treasure and VPs) either will not fit at all, or will have to be jammed in pretty tightly.

Personally, I put Dominion, Intrigue, Seaside and Alchemy into two "long boxes" that you see used for CCGs, with little labeled tabs I printed from BGG separating them.  This takes up a lot less room than the 3 large boxes and half-size Alchemy box, and makes the game portable.

Prosperity is still in its original box since I'm out of space in my long boxes.  I keep all the Kingdom cards in their original slot, but keep Colony and Platinum in some of the larger unused slots rather than the ones labeled for them, because I don't like the tight fit.