I have used this control scheme and not had any problems with it. Control dampers have pressure drop, even wide open (see damper authority), so the pressure drop is already there. If the differential pressure across the outside air damper is controlled, wind pressure, seasons and filter...
Whatever you do, the doors to the server room (and the walls!) need to seal really well. As BronYrAur says, vapor pressure is an issue. You may need to put vestibules on the doors into the server room. Typical server room cooling systems are not designed to handle much moisture (latent) load...
I agree with LittleInch that the coil pump will not increase the pressure at P2 above P1 as long as the main pumps are running and there is flow through them.
The “Pete’s Plug” is a pressure/temperature (P/T) opening that self seals and is used to insert a pressure or temperature gauge into the...
