Can I leave Match Chat?

Yes. During a match, press P to bring up channel settings. Click on the filled speech bubble next to "Match" to remove yourself from match chat. You can also remove yourself from team chat or voice chat in a similar fashion.

The settings will persist across matches, so you don't have to do this every time.

You can also press Ctrl+Shift+C to hide the chat. It also persists for the entire session.