Nah man... I'm pretty sure the TT-01 will spontaneously combust when it sees Lipo power. If your car wasn't infested with tamiya blue then things would be different..
Say.. if your TT was purple... then things would be alright..
Generally speaking ray - the troubles arise on belt cars. Shafties usually mount their batts longitudinally ON the chassis plate. Either strapped or with a plate. The TT tub should have plenty of room.
belt cars however, usually tuck the cells transversely across the chassis .To get them right in, they tuck them under the bulkheads. The bulkheads are a tight fit and usually shaped to fit the cells. The Lipo packs are somewhat square edged - Ie. don't fit without major dremel work.
The TT will be fine.. (Oh crap - if it doesn't i see ya around. Damn...)