Looking at the code, I think it's possible. I know for a fact that ships can have more than one trail (the max trails for a ship is defined by MAX_SHIP_CONTRAIL), and AFAIK the only thing they do differently when the trails on a ship (in the trails.cpp, no idea yet what's going on in shipcontrails.cpp), is if it's your ship and you're not looking backwards.
And so if the code parses the ship.tbl and the weapons.tbl in the same way regarding trails, all you do is make a second $trail: entry. If that won't work, then AFAIK, you'd be stuck with having the missile as a ship, and having to spawn it manually in FRED and set it to kamikaze.
EDIT: And looking at the shipcontrails.cpp, it looks like if the object is a ship, it doesn't really use the trails.cpp for anything other than rendering or something. Disregard everything I said, just to be safe.
