Having had both arms in plaster (though not at the same time) I'd pretty much guarantee that you will need your arm for something. Tying a tie, shoelaces and even buttering toast is much easier with two arms.
I don't think being in a cast will have any affect on a gynaecomastia operation though. The cast will be there to protect the arm, the only thing they might do is bag it so the cast doesn't get any blood spattered on it. Also, it may be hard for them to insert a line in your vein if the hand in the cast has the 'best' veins.
What I would say though, is that with one arm in plaster and limited movement in your chest after a gynaecomastia operation, you're gonna be very vulnerable and might have trouble doing even simple things until you can move both arms freely.
