Alexban,
I have just done an A320 self sponsored type rating. The guy I was paired up with did exactly that. However, we both get it on part 1 of our license anyway. He remained in the LHS and I in the RHS. Stops all the swapping of seats a gives you a consistent perspective of the Cockpit layout etc.
His experience is Captain of Large Boeings and Corporate Jets. He is looking for an A320 LHS position at the moment.
BR.