Does StreetPass still work if a DS game is suspended/sleeping in a 3DS?

No - StreetPass will not work if a (regular) DS title is suspended.

StreetPass will definitely occur if a 3DS title is suspended with the system on, closed, and transmitting wireless. (I've had this happen with Ocarina of Time.)

StreetPass will also often work when the system is open and you're actively playing. I've had this occur many many times when using StreetPass Mii Plaza (Plaza and Find Mii II), and even in Street Fighter IV 3D.

Streetpass works that way with some 3DS games, but not with regular DS games.

Certain DS games have something similar to streetpass called tag mode. If a DS game with tag mode is inside your 3DS, streetpass will be disabled. If a DS game without tag mode is inserted, you will still be able to use streetpass with the game inside.