You will invariably hear different responces on this topic, but allow me to be the first to reply. I'll start by agreeing with you: it is not nearly as hard as it sounds! First I'd like to ask, how far along are you, even if it's just right hand alone? Also, it won't make too much difference but what is your general skill level? I'm sure others on the forum know you better than I do, but what are the other pieces you're working on?
1) The bass is actually REMARKABLY easy to learn after the right hand; in fact there was very little learning going on when I did the piece, the left hand just "made sense" and it wasn't long before it made the moves automatically.
2) It took me approxiamently three months to learn the piece (and I played it in a recital a month later), but I admittedly started when it was still beyond me technically. I'm sure any slightly more experienced pianist than myself could have it memorized (which is not difficult at all, given the simple theme-and-variation set up) and up to preformance level in a month or two.
3) Again, it would be helpful to know which other pieces you're working on not only to tell if it'll be too much to add Campanella but to see if Campanella would fit into the rest of the program better or worse than the Rach preludes.
Overall, though, I think it's realistic to have it done by May and in satisfying condition.