The main effect of props is that it makes the aircraft easily identifiable to a submarine in anti-submarine warfare, however that is not to say that a jet engine aircraft will not be detected.
As far as an MPA being counter-detected by radar, props or jets will not make much difference to its signature.
There are numerous benefits regarding aircraft performance, ie instant power, or the ability to reverse etc, and prop driven aircraft are more suited to smaller, rougher, airfields, as found around the South Pacific, NZ, etc
Y_G