You don't want to run the Cp-3 at less than 3 psi of fuel pressure at the inlet for extended times but it is a lot less sensitive than a VP-44.
The CAT filters geenrally are high flow enough you don't see much if any pressure drop on stock or a little bit more fueling. With a good LP it should still hold 7-8 psi most of the time.
The CP-3 is still fuel lubed and cooled so a good supply of fuel is needed. The CP-3 will prioritize fuel to the rail rather than cooling\lube circuits so running it with low pressure is not a great thing to do. As a rule about 5 psi is the limit you would want to pull supply pressure down to for any length of time. In addition to lube\cooling lack of flow at the gear rotor pump has a side effect of causing cavitation in the pump. Cavitation is bad any time as it will beat the gears and wear plates up. Any metal fragments that get sluffed off end up right where they don't need to be, in the injectors. The more pressure the better to limit any potential problems.
A gauge as close to the inlet of the CP-3 is still a good addition to monitor filters and the LP delivery.