I really think it depends on the cat, some will, some won't, I sure wish
you the best of luck, I know how hard it can be to trap cats. I have a
calico that won't even go NEAR a trap, and keeps having kittens every 4
months. But I have had other's that were trapped more than once.

Let us know how you make out,

Good Luck, and bless you for trying to help the cat,

Aimee