I carry a bottle of "bar's leaks liquid aluminum radiator stop leak" in the trunk of my car for a emergency situation only. I would like to know if I have to use it one day then what are the chances it will clog my cooling system? Is the product safe or is their a good chance it will harm my cooling system?

Possibly--I would not use it. It's better to follow a good preventive maintenance program, so you don't need to carry that stuff around.

Read the bottle it will tell you how much to put in . Do not just put all in unless it tells you too. If you put too much YES it will clog the system.
I have used it and it worked.