Considering how frequent Bristol motors were used in FAA aircraft, from the Flycatcher to the SKA and Albacore it's noteworthy that the Hercules never saw much fleet service.
Let's change that. Starting with the Fulmar and Albacore specifications, let's have the FAA demand the Hercules for its aircraft. This will likely have the Swordfish in service longer until the Hercules is ready. And a Fulmar Hercules would be the only single engined fighter thus powered. This presents issues of fighter suitability, though the Beaufighter did fine as a twin.
The only problem I can see with the idea is the first Hercules were not built until 1939 and the Fulmar Mk 1 enters production in the same year.
There would be a delay in developing the Fulmar
Fulmar was not ordered because it was the best Carrier fighter available - it was ordered because it was the only then 'modern' fighter the Navy could get its hands on and one that could be built as quickly as it was.
Now the subsequent Mk II might be built with a Hercules II (1375 HP verses 1300 HP of the Merlin XXX) although the change in engine would likely delay the introduction of the MKII but as to what impact this would be I cannot say?
Where there may be a positive improvement is the Barracuda - it was going to use the RR X engine but this was cancelled (I blame the Germans) and it started life using the then Merlin which was not nearly as powerful then as it would later become and so the early Barracuda was seriously underpowered which delayed its introduction.
Perhaps with the Fulmar MK II and possibly even the Albacore using the MK II Herc the Barracuda is designed earlier to use the MKIV Herc (1,650 HP) and its power issues are overcome.
What I would say is that the Merlin/Griffon engine line benefitted from a great deal of man hours and 'treasure' being lavishly expended upon them.
But the Herc was a single stage Super charger and as the FAA aircraft are not intended to fight up in the 'Gods' like Spitfire was - it might mean that the FAA has more control over development and availability?