Can I just use banana instant pudding in my extender with a white cake to give it a banana taste?

Can I do anything with instant pudding in buttercream to give it a banana taste? I am assuming bananas will not hold up well as a filling.

Banana pudding will give it a slight taste, yes.

I think I have seen banana flavoring at the grocery store - can't promise though.

If you use pudding mix in buttercream, make sure you dissolve the powder in a few tablespoons of milk first. If you don't, your buttercream will be extremely gritty and grainy. Not pleasant!