We have applied positron annihilation spectroscopy to study the formation of Ga vacancy related defects in Mg and Mn doped bulk GaN crystals grown by the ammonothermal method. We show that Mn doping has little or no effect on the formation of Ga vacancies, while Mg doping strongly suppresses their formation, in spite of both dopants leading to highly resistive material. We suggest the differences are primarily due to the hydrogen-dopant interactions. Further investigations are called for to draw a detailed picture of the atomic scale phenomena in the synthesis of ammonothermal GaN.