If all he wanted was to go into Impel Down, he could have just done it instead of becoming a Shichibukai first. None of the Marines at Impel Down were "fooled". They immediately realized he was betraying the WG.
Edit: Yeah, as I thought, Blackbeard didn't use his Shichibukai credentials to get into Impel Down. He stole a Marine ship.
http://www.onemanga.com/One_Piece/542/03/
I think the betrayal is an important part of the plan, because it has destabilizing effects. The WG was counting on him and his powers when they "declared war".