I obviously can't speak to Beethoven, but I have witnessed a couple of very successful modern composers (of classical music) - just in passing now and then, I didn't sit down and study their methodology, but can definitely vouch for having seen extremely talented and successful composers sat at a keyboard instrument tapping out ideas.

No doubt they, like Beethoven, would be much more able to compose some if not all in their heads than i would be, but it doesn't mean they don't still find useful, at least sometimes, basic stuff that amateur composers do.