What happens if I don't renew my Coin PEL? Can I still continue using Coin?

Yes. You can continue development using the last version of Coin (or any earlier version, if you want) that was released while you were a registered PEL holder. Version in this context means "release with a unique version number", so for instance 1.0.0 and 1.0.1 count as different versions.

Of course you are not allowed to use any version of Coin that was released after the expiry date, and you will not get any more developer support.