If you're worried about your IP being "leaked" you have no idea what an IP is. You can literally grab everyone's IP using the console commands to list the players.
Status no longer reports user Ips as those are hidden through some steam routing, I'm not sure if rcon status still reports it but that would be limited to server admins. If you open the steam overlay while in CS it shows some of the details.
No, most multiplayer games and services these days only share your IP with the server, and not with other players.
Leaking your IP to someone malicious can mean DDoS attacks and rough geolocation. IP can be a good narrowing to find your address when combined with additional information.
SC2 is not a game one would expect to leak your IP and is a valid, small concern.
Being aware of the small risk you're taking with one person (the server owner) versus being unaware of the risk you're taking with many different random lobbies.
Server owners are more likely to ban you than DDoS you. And it's a single digit number of people with access to that information vs hundreds in random lobbies.
The risk, while still small, is hundreds of times greater than a private server.