Yes, it is enough. Generally, the default handling of connections on Linux is enough but having ufw can't hurt. Certain developer or server software may not work unless you add UFW exceptions for them. They don't know how to do this on their own.

By default, without a firewall, any program can communicate through any port it wants as long as it can bind that port. Ports that are special or low-numbered (e.g. TCP port 21 is reserved for FTP) require root to be bound. Otherwise, a program can bind any port that isn't already in use by something else. All incoming connections to a port that isn't bound will be refused and the information discarded.

Edit: Your router also usually has a firewall that is strong enough for most everyday purposes.