Can friction increase the mechanical energy of a body?

No.

Total energy = KE + PE + WE; where WE is due to work done by the system against friction force. Thus

E - WE = KE + PE;

so that the more work done (i.e., more friction force all other things equal), the less total energy will go into kinetic and potential energy.

Mechanical energy only gets larger if there is an inelastic collision like an explosion which converts chemical energy into mechanical. 

So the answer will be ambiguous as friction can increase the mechanical energy depending on how we define the system and the frame of reference.