Not a bad idea for the first and maybe the second movement. The third is definitely for advanced students. Nevertheless if you have command of a few basic keyboard skills, learning to play a passage or two from a really advanced piece can be advantageous for later work though few teachers will recommend it. Let's go for the ultimate but assume you're not actually taking lessons!

How about Ravel's Gaspard de la Nuit? Certainly one of the most difficult pieces ever written. It's quite possible to work productively on the first page of 'Ondine' and as with the Moonlight sonata, it's exhilarating to hear yourself play that exquisite tune - distilled as it were, into its essence. Plenty of other possibilities such as passages from Mozart piano concertos. A bonus is that one's appreciation of great artists becomes much enhanced.