The RAF was well served with the Hurricane and Spitfire so the only role for the Gloster is with the FAA who already knew they were short of an effective fleet fighter. The Sea Gladiator was ordered as a stop gap until the Fulmar came in and they also knew the Fulmar was marginal for the role (falling 6 months behind planned production too) and were seeking a Sea Spitfire pre war and Sea Hurricanes later.
Equally the limit on the Gloster was the Mercury. It was the only feasible choice at the time but was never going to give more than 950bhp whatever improvements one might throw at it.
So the sales pitch has to be an interim Mercury Gloster MkI with a significant redesign to allow a heavier engine in a MkII later on, maybe with 20mm cannons, constant speed propellor and a fully folding wing in 1941.
No foreign engine is going to be chosen pre war and the Mercurys weight can only be matched with a Perseus which is no great change. The Taurus was going to be in FAA service with the Albacore so the MkII would be a Taurus powered job (with the possibility of Merlins as used in Fulmars IOTL).
So, couldn't Bristol have used their Hercules engine instead (originally type-tested in Jan 1936, flight-tested in 1937), or simply put their Centaurus engine into production at an earlier stage (which was originally type-tested in July 1938, but its production was placed on hold until 1942 IOTL, owing to the need to prioritise the Bristol Hercules as the primary powerplant for the RAF's Bomber Squadrons)? Or simply utilise both options, with the earliest Gloster MkI powered by the Hercules I engine, and other Mks of the Gloster fighter aircraft (or its newly designed successor), later on in the war, powered by the Centaurus engine instead?
I am not sure of the fleet carriers deck lift dimensions but the Gloster is not far off Sea Gladiator wingspan if only the tips are folded so possibly a Sea Gloster need only minor changes to the original. Range may be an issue and drop tanks are not a period option so extra internal tankage may be necessary. We must also factor in the weight of self sealing tanks (unless they were on the original) installing armour, hook and minor naval kit.
So what would they get. A fleet fighter which is better than both the Gladiator and Fulmar in the MkI and up to Sea Hurricane in the MkII.
From the MoD point of view you lose Gloster built Hurricanes so the RAF has fewer Hurricanes and the Gloster design staff are doing the MkII at the same time as their jet designs.
I can't see the FAA getting a better deal at the time but who would take up the slack in Hurricane production?
If they stick with the Mercury engine, then yeah, pretty much. If they went with the Hercules engine though, the MkI version of the Gloster fighter aircraft would probably be a fleet fighter (or land-based fighter-interceptor) on a par with, or superior to, Grumman's F4F Wildcat (/Martlet) or Republic's P-43 Lancer; but unlike these two aircraft, one which would be ready to enter production and active service in either 1938 or 1939, prior to the outset of WW2. Later Mks of the Hercules-powered Gloster fighter could probably attain similar levels of performance to Grumman's F6F Hellcat. And if they went with the Centaurus engine (or switched to using this engine for later Mks of this fighter aircraft during the war itself), you'd have a British fighter plane with comparable performance to the FW-190 A-8 (probably entering service at around the same time), and the potential to have an aircraft (Gloster's appointed successor to their F.5/34 fighter, fully-redesigned around the Centaurus engine, and entering service in the later stages of WW2) on a par with OTL's Hawker Fury/Sea Fury and Republic P-47 Thunderbolt (or the Grumman F8F Bearcat, if we want to continue the direct analogy between these two fighter aircraft lineages).
Regarding the designs for the jet fighter program though- if they were already in full war production of their own line of fighters ITTL, I'm not sure that the Air Ministry would bother approaching Gloster with the contract. IOTL, the Air Ministry approached Gloster specifically because their design department wasn't working on anything else at the time, allowing them to invest all of their efforts in the Ministry's jet fighter program. ITTL, they'd have their hands full- they wouldn't have the time or design capacity to devote their efforts to the jet fighter program. So, who would the Air Ministry turn to instead? What about Martin-Baker Aircraft? After all, the Air Ministry's E.28/39 specification for their jet fighter went out at around the same time as their F.18/39 specification IOTL (which probably won't be given as high priority ITTL), and Martin-Baker's fighter design department wasn't working on anything else at the time.