The fundamental issue with PAK joining the saudi led bloc is that it is meant to control Iran-Iraq-Syria-Hezbollah(in Lebanon), and certainly Yemen where HOuthis are in power on the ground and for 20 months Saudis have been committing war crimes.
Not just that Iran is our immediate neighbour, PAK also has around 20 percent Shia population, how would they think of it is a serious thing.
Besides, Should PAK play a role, that must be of a mediator between Iran and KSA so that the bloodletting and terrorism may somehow be rooted out of the ME and all the Muslim states, to any possible ambit.