Copying it does not allow him to master the technique, no. It does let him figure out how to use it, though. Sasuke's Shishi Rendan was made from copying Rock Lee's techniques. He was not as skilled as Rock Lee in taijutsu/speed, therefor had to change it to fit his skill set. But he still copied the moves and learned how to do his own version of it.
Kakashi having copied 1,000 techniques does not make him a master of 1,000 techniques. But if he wished to do so, he could master any of those 1,000 techniques that he so pleases, given he puts in the training for it.