I definitely helps physically - balances the cortisol in your bloodstream, calms your muscles for restitution, makes it easier sleep, etc.
"Mentally" is also in a sense "physically" as you will probably have an easier time talking to people after exercising, worry less, etc.
Working out doesn't help your personality though. You shouldn't expect to suddenly drop your avoidant ways by jogging a couple of times per week, though you might gain some confidence from being healthier/stronger