Why do you need to have a 4-pole ATS when the ATS has its sources coming from both the utility and emergency generator both of which are solidly grounded?
In the simple case (ie no GFP) you dont, as long as the single installation N/G bond is after the ATS, a three pole transfer switch is all thats needed.
The most common case that requires (ie for regulatory reasons) a four pole transfer switch is where one genset feeds two or more installations, where each installation has its own service. The four pole switch is necessary to prevent the ground wiring being a parallel path to the neutral, as there are multiple N/G bonds.
The presence of GFP on its own doesn't require (for regulatory reasons) a four pole transfer switch, but (and I'm off personal experience here, relying on the opinions of others) generally, the installation works much better with a four pole transfer switch, much better being defined as avoiding nuisance tripping.