Well if you've got cats I'd be very wary of bringing a strange dog into the house even if the dog is used to cats. So yes I think it's a bad idea.
My dog grew up with my two cats, both of whom are no longer with us sadly, and although she got along fine with both of them - having quite a loving relationship with one - she seem to be terrified of other cats and will growl and lunge at them. I'd never take her to a house where there are cats or bring another cat into my house.
Of course it is possible that DS's friend told him that they were going on holiday and DS has just taken it on himself to ask if you can have the dog to stay. It's possible the dog is already booked into kennels and you might be worrying about nothing.
I've spent the last 5 years trying to convince DH to let us have a dog. But now the idea of actually having a dog, the poo, the responsibility is a reality, I don't even want it for a short time! I actually want a baby, not a dog So I've decided we will decline.
The parents definitely asked DS to ask us if we would like to look after the dog. I might ask if DS2 can take it for a walk with them sometime, as he really, really, really wants a dog.