He's have a much more extensive body of work, but it is hard to say how things would play out. His romantic and jazz sensibilities might come up to the surface enough for peers to overlook him. Or, like Rouse or Glass, for example, he could maintain a comfortable niche somewhere between the critical and public consciousness.
His film music alone qualifies him for this. And his concert output, taken all together, concerti and overtures and the like, is quite a body. Personally, I think that it does get him a seat at that "classical" table you refer, but perhaps not a very high seat if taken only by itself. I do believe his best, most worthy work is for film.