There are two kinds of smoked salmon. Hot smoked and cold smoked.
Hot smoked salmon is cooked through and has a smoky flavor as you would expect. You usually see a thick fillet (6-8 ounces) of salmon hot smoked.
Cold smoked salmon is not cooked. It's eaten uncooked and smoked. Lox, that folks put on a bagel with cream cheese, is cold smoked salmon. It's usually found in thin slices.
You can use either one in sushi. There is no rule that fish used in sushi must be raw. Some sushi is made with those imitation crab thingies - surimi.
In fact, you can make sushi with just vegetables.
For a twist, make a sushi roll with roasted red pepper, calamata olives and fresh basil leaves.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan