We got a cat from the RSPCA and I know they like to check out the home and surrounding area that the pet is going to before they allow anyone to take them. So unless, you can arrange a visit when your parents are out it might be a bit difficult.
Give them a ring and ask. Good luck. Sorry to hear their current cat isn't well. We lost our cat a few months ago and it's still very strange without her here. We get ourselves so attached to these animals don't we? I'm only just coming round to the idea of getting another pet but not sure if it will be another cat or something else as yet.
we looked into getting one from them and where told that they would not send one home unless you have visited twice also they will want to check out wher the cat will be living as they will not let you have one if you live near a busy road or a school
they will also not let you have a kitten if you have a child under 5 or let you have a cat if you have a child under 5 ( it's a wonder they actually get to rehome any cats at all