Would it be a smart idea to replace the stock air box on my 96 XCR600SP tripple and place K&N type filters on each of the carbs instead? I love the look of it and wondered if I would pick up any power from it. Also would I need to rejet if I do that?

Nope Not a Smart Idea.. Looks Kewl!! Good for for looks!! IMPO Leave the Airbox. Fresh Cold Air.. Is Where it's at!!! Only run Filters if there is a NEED to..

Well when i took my airbox off the carbs were really dirty and so was the inside of the airbox. I know theres no filter in there so i figured it would be better for the motor if it actually had some filtration

If you can still feed the filters cold air then you wont lose performance. If you ever get into doing lots of jetting and pulling the carbs off alot it gets annoying with an airbox.....filters are extremely nice in that aspect.

wouldnt the air flowing into the hood vents be feeding it cold air?

It would be pulling warm air off the engine. Not enough cool air would get to the filters through the vents. Also it hard enough to keep real fine snow out of the stock air filters and air box, now think of how bad you would suck in snow with just a filter system.

You would be better off looking into a high flow air filter system. Something likes this: High Flow Air Box