Fire up GZDoom and go into Options -> Player setup. Try to change your player colors. It seems that the color doesn't update. This affects the player paperdoll in the menu, as well as your in-game player sprite (you can see for yourself by activating the chasecam - the player sprite's colors do not update).
If you restart the map, however, the player's new colors will be applied.
In OpenGL, the color updates are instantaneous.