Can you discharge a 3s LiPo battery from both its main plug and it’s balance plug?
Yes, this is fine, provided you don't draw current in excess of the normal balancing current that the balance wires and connector are rated for. That shouldn't be a problem if it's just running logic and radios, might be more of an issue if you were wanting to run some high-powered servos.

Note that it it's important to only draw from the outer balance wires which are directly connected to the overall pack + and -. If you were to tap off intermediate wires (to get a lower voltage) you'd quickly unbalance the pack.