Does hugging Leonardo da Vinci yield any benefits?
Solution 1:
I, too, missed this moment1 and was a little bit annoyed, he gives you such a hurt look afterwards too...
Anyway, at the time, I investigated and it seems that this has no effect on the game outside this cutscene. This is apparently also the same for the other quick time events in the game.
Good job too really, since there's a only a few events in the entire game and they all catch you unaware; if they were made important it'd be simply cause too many problems for players.
1PC control issues, rant rant rant