Rats and cats in the same household?

Sorry in advance if this topic has been discussed to death in this sub. I am considering getting a group of rats sometime in the future, but likely not for several years. I currently have an elderly solo chinchilla in a large critter nation and don't really have the space or additional time to devote to a second cage/group of pets. One of my main concerns is that we do also have two cats, and I know rats are intrinsically fearful of cats and their smell. However, our current cats do not bother our chinchilla at all and pretty much ignore her. Of course the cats are also removed from the room any time the cage door is open or she's let out for playtime. Assuming the cats behave the same way toward rats, is this a doable (and humane) setup? Or would the rats truly need their own room that the cats have no access to so they can't smell them? Again, I wouldn't even think about getting rats for years into the future, and if cat-rat room sharing just isn't kind to the rats, I wouldn't want to put them through it.