I want to upgrade my Competition Electronics Turbo 35 to charge LiPo batteries. Will it charge a 2s1p lipo? I'm new tot the lipo world.

Yep, there website says 1 or 2 cell (1s or 2s)

your turbo 35 can only be used to charge regular nicad and nimh batteries unless you have the lipo upgrade ,go to competition electronics website and you will find the info for the charger and the upgrade cost .i'm not sure if it will do any balancing so you may need to pick up a balancing charger