of course nababawasan yan, kahit pa through third party ang connection, the key word is may connection.
example maglaro ka ng HON, LOL or whatever acronym game, yung mga data na need ng game like updates of position, stats, etc etc syempre ipapadala yun sa game server, then the game server will in turn send in data to you with regards data from other players you are playing with. that consumes bandwidth.
as to kung gaano kalaki, depende to sa game. some games most of the data is stored locally so the only connection needed is mga updates like yung mentioned earlier. pero ibang games need more data as not much data is stored locally so of course these consume more bandwidth. kaya minsan pag naglalaro ka ng ibang games mapansin mo mabagal masyado ang galaw mo and ang galaw ng screen, thats probably because your connection is not yet done downloading the needed data for the game