The biggest problems I see are the time left alone and being a single cat. This situation would work fine if you had already established a long relationship and you knew their behaviors, but a new cat, even an adult one, needs to bond with its new human companion, and a few days here and there isn't going to do it well. Then there's behavior, you don't know any of its history and how it might do in your home alone. It could be totally fine, or it could get scared/mad/bored and start tearing up things or even hurt itself. Which leads to the next point, while some cats can be solitary, most do like another companion to play with (can be a dog, sometimes they pair well, but usually cats) so they don't get bored.

I think the problem for you isn't if a cat would work, but finding the right cat, and unfortunately you can't know how they will do thrown into that without time to help them adjust.