I don’t know about Copay, but you can just leave the Bitcoins in Coinbase if you are not interested in trading. However, even though Coinbase seems to be a good company and is probably secure, there is always a risk that they will get hacked, go out of business, or have some kind of problem that results in the loss of your Bitcoins. It’s generally a bad idea to store Bitcoins on an exchange but I think Coinbase is probably one of the more reputable ones out there.
If you want to be even safer, you can move the Bitcoins to a paper wallet or hardware wallet where you will control the private keys. There will still be some risk if you don’t getthat set up correctly.