Radios that are set to output 50w are designed to do so when supplied with 13.6 or 13.8v, and at that voltage might draw 13A while transmitting. When the vehicle is shut off, the battery is going to supply closer to 12.6v when fully charged, and at that voltage, the radio will draw fewer amps; maybe 10-12A. And that means you will probably be transmitting at a little under 50w. You would have to measure to find out more precisely. The FCC won't approve a GMRS radio manufactured with the capability to transmit more than 50w at 13.8v. That means manufacturers aren't going to risk producing one that outputs 50w at 12.6v, because it might exceed the FCC limit when being run in a vehicle with an alternator putting out 13.8v.
That means, if you want full power output from your radio, it needs to have a power supply that produces the correct voltage, and that can meet the amperage needs of the radio. For your 50W radio, you would want a power supply that can produce that full 13.8v, AND that can provide 15A current (which is probably what the radio is fused at).