If you had 5 planets in an X shape , moving the HQ from a limb to the center would raise your total max allegiance from 480 to 510, which isn't much.
9 planets in an X shape, moving the HQ from the edge of a limb to the center would raise it from 750 to 870. (16% bonus on average to each resource collection)
Obviously an X would be rare, but this gives an idea of the kind of gains it can bring.
There's a few factors to determine if it's a good idea: The the size of the galaxy, the vulnerability of said planet (If your hq gets sacked without another one being built, it will do a lot of income damage), and the intended length of the game. If you plan to attack aggressively and have the battle end in 30 minutes, it may not be a good idea, but if you're playing at a leisurely pace, and maybe aim for a several hour game, then you should definitely move your hq around.