Online Lobby

Based on my estimates: Less than what's needed for browsing the HeroesWorld forum.

One game is a one-time transfer of a map to/from the server, for example:
90 KB for XL+U and 250 KB for G+U (this is for random maps. Custom maps can weigh 1.5 MB or more)
Next comes the exchange of a ridiculous amount of bytes, including global chats.

In general, 2G on a mobile phone in the middle of nowhere handles the lobby.

This is all for a single player.

Honestly, I was very surprised when at the last CIS (I think) event they played not through the lobby to save traffic.