You have to converge the total energy and other physical quantities of interest with respect to the mesh density for a given pressure applied. I guess this is the only way to actually see if there exists any significant dependence of the density mesh cut-off on the external pressure. It is very likely to be insignificant for low pressure, and it might become an issue when the pressure is high, but this is a matter of numerical experiment to figure out what is low and high for your specific system.
