Sometimes yes, but not always. And in a situation where someone might be evicted they are probably hoping there will be a last minute reprieve.
I do know what you are saying and some people do ring and ask for advise in some situations, what I say to them is put the cats on the list waiting to come in and every day you are moving up, you can always change your mind or if they ring you before a final decision is made defer bringing in the cat but you will still be top of the list.
However many of the cases we deal with there is no chance that they will win a reprieve and it is always those types who don't bother until the last minute. Then usually tell us it is our responsibility to take the cat or more usually cats.
What make me even more annoyed is when they have known for months there is a problem yet it is a mum and kittens that needs to come in. At least had they bothered to get mum spayed the problem would have been more easily resolved.
Another problem I find is relations purchasing kittens for usually the elderly and within days the new owner cannot cope and we are asked to bring in the kittesns, of course the person who purchased the cat does not want to know.
Very recently a man who lives in London purchased two kittens for his very elderly mum to keep her company, she just could not cope but he did not want to know and just said I can't do anything now I live in London. It put s us in a very difficult situation when you have a very elderly person crying I can't cope. Of course somehow we do help but it is at the expense of another desperate cat/kitten.