short answer, no
you need to have your coins in an open unlocked wallet to stake
Do stakes build up over time? Like let's say I hold my HBN for a year. Could I then take them out and get the accumulated interest?
I'm guessing that since the wallet addresses would be different in that case, I'm just giving the interest to Cryptsy aren't I :

Stake do build up overtime. But each time you stake it splits the block in half with added interest. So a 100 HBN stake would give about two blocks of 51 and the 100HBN block would be gone. This happens over and over and the blocks get smaller and smaller. Eventually they turn to "dust" and take significant amount of resources from your cpu. So you would want to recombine blocks. Also your wallet needs to remain open in order to stake. View this wiki page for complete details