The only reason he couldn't transform was because he didn't have a tail, and even Bulma said that the Blitz Machines' function was to transform him without the need of a tail, and that it didn't have anything to do with strength. He had to undergo immense training with Bulma and he cant do it by choice like Goku Above me - You're terribly wrong. No, Vegeta is uncapable of being able to become SS4.
btw there was already a thread on this recently Janemba4eva 00:00, Septem(UTC) So in GT Vegeta could probably handle the transformation on his own if he had a tail. I think he'd be able to, since in DBZ his SSJ2 was comparable to Goku's, and it's never said that SSJ3 is a prereq for SSJ4. You know why because gt is fake it is not real and go back to the original db when goku was a kid kami got rid of hi tail never to grow back again and now goku gets turned into a kid and they trie to oull his tail out