I would say no, unless your don johnson adn then I wouls still say no. This isn't the 80's and sport coats are just too nice of a garment to be worn with a t-shirt, you are better off the keep wearing them the way you are now. I always say if it's not broke then don't fix it and your style seems to be working fine to me so don't go changing it.
Show us. We'll give you an honest opinion. Some people can pull this off, some can't.
I've run around (Rome) at night wearing a Hugo Boss suit with a t-shirt. It worked well enough to get me into a couple of pretty exclusive places.
The look doesn't depend entirely on the clothes. Depends on where you are, and more importantly - what the rest of you looks like.
Don Johnson, David Duchovny and Bruce Willis can do this. Most of the rest of us just - can't.
Face it fellas...We aren't Them.
So!! Go put on your best t-shirt...Put on your best Sport Jacket... Take a picture and tell us where you'd like to go with this ensemble - and we'll judge.
Perhaps I watched too much TV in the 80's, but whenever I see someone wearing a T-shirt with a sport jacket or suit, I think of this. Not sure I'd want the back of my neck dirtying up the inside collar of my jacket as I don't like dry cleaning them often.