OK, I see what you mean now; sorry for the misunderstanding.
Yes.
But it really isn't. After all, if you were to put a USB connector onto the board but in reality it carries a different kind of signal, you're creating a confusing situation that will bite you or someone else in the posterior sooner or later.
If you feel adding pins would take up too much space etc., you could do something with pogo pins. All you need is a couple of pads, in that case. You can make them pretty small. You may be able to find pogo pin headers with a narrower pitch than 2.54mm, but I haven't specifically looked.
Oh man. There are so many connectors out there. One thing that comes to mind is a narrow-pitch FPC. E.g. a 4-pin 0.5 pitch FPC connector can be something like 8.5x6mm. That's not particularly big. Of course, smaller = clumsier, but it'll work for debugging etc.