Cut and polish improves the paint 100%. There is a technique to it and it's best left to a professional. Once done the sun will highlight the curves better, and the paint will have that glass-like look everyone wants. You should wait a minimum three weeks to cut and polish, and longer if you can. My car was spayed a week ago, and I'll wait till the spring to do the cut and polish.
By the way, the door gaps and body lines on your car are exceptional. That body line where the fender meets the door can be tough on some 69's. Great job.