Oh, I'm sure you could pull it off. Doesn't mean a Kirk vs. Picard battle would have all that made much sense nor would it have been very popular. And knowing how many Hollywood writers pen action scenes and scenarios it probably would have been dumber than a Paris Hilton lecture on quantum mechanics.
Mind you, we're talking about a movie where a whirling, swirling energy ribbon contains each individual person's idea of paradise and it can destroy a vessel that gets too close, but organic material like bodies are absorbed into it in one intact piece....but I digress.
I think the way they actually pulled it off was adequate and entertaining if very rushed. The whole Kirk-Picard Nexus sequence followed by the final confrontation with Soran happened so quickly that you didn't get enough time to enjoy the captains of the two different eras and series getting to spend time trading ideas and experiences. Whether you did or didn't like how Kirk eventually dies at the end of the film the entire Kirk-Picard section of the film felt too sped up after all those years of wanting and wondering and wishing that our two favorite Starfleet captains would eventually find some way to join forces.