RE: Break-in a rebuilt engine?
Of course you should give the engine a short break in procedure with some extra oil in the fuel. If you use the same ring it will fit with the sleeve and the engine will develop its full power very soon. Just give the new piston a little running time to seat properly to the sleeve.
It is very usual that manufacturers recommend a run in every time after taking the engine apart and reassambling it. This may be more important for non ringed enginges.