This is a weird question because "able to play" the sonata is somewhat imprecise in terms of wording. Do you mean if she actually played it well, or could have if she wanted to?

Anyways, I don't know if there are any sources about her playing. In any case, the Moonlight Sonata is relatively easy to play (especially the famous first movement). There are some arpeggios and runs, but in the repertoire of musical literature, or even Beethoven's sonatas, it is not a technically challenging piece. However, it requires lots of interpretive skill in terms of the ability to choose dynamics, phrasing, etc., reason that those choices make the piece sound the best, and carry out those choices. That's much trickier. Was Guicciardi able to execute the technique necessary? Very likely. Was she able to make wise musical decisions? No one can say without a recording or description of her playing.