The problem with fighter bombers based on say the Me 109, Spitfire P40 is that these aircraft were too small to carry a bomb load that was worthwhile without loosing performance; speed and range. They don't have range to begin with.
A Fisher P-75 or Boeing XF8B-1 has range, even with bombs. They are also not going to slow down much with a load.
When the Luftwaffe worked out their bomb shackles they had a fighter in the Fw 190G that could haul a bomb to a target deep in enemy territory 1000km away and return. Speed loss was about 50km/hr which was almost restored with C3 einspritziung. They used the aircraft with blind bombing systems and it was a moderately sized fighter.
The Bf 109, P-39, P-40, Typhoon, and Fw 190 were all less capable fighter-bombers than the likes of the P-47 and F4U in terms of combination of performance, load, and range (the Tempest and Fury might be more competitive but still shorter legged on the whole and I'm not entirely sure where the F6F might fit in).
The P-38 takes the load+range capabilities a bit further and the F7F further still while both were adaptable to nightfighter roles too. (similar for the De Havilland Hornet as well)
The Fw 187 might have developed into something along the same lines as well, likely more akin to the P-38 than the later F7F (or Hornet).
The Me 410, Ar 240, and Mosquito as bombers/fighter-bombers seem to fit in more of an odd middleground there as none was really capable of performing day fighter duties, unlike the P-38. (granted, the Hornet and F7F were no longer capable day fighters by the time they actually saw combat, but as late WWII aircraft they were more competitive even during the transition to early jets)
OK, R-2600 powered F4U?
Even if you go for the low altitude ground pounder, the R-2600 gives up too much and it never got a WEP rating or water injection. Please compare the R-2600 power at 12,000ft to the Allison, then figure in the added weight, the added drag and then see what real advantage the plane would have over a P-40. Unless you stay really, really low AND have good escorts flying top cover, this doesn't look like a good option.
I was thinking in terms of both the British and Soviet lend-lease P-40 deliveries in the event sufficient R-2800 production wasn't initially available. Admittedly, this seems unlikely (in as far as Corsair production outstripping R-2800 production). The 1850 hp single-stage R-2800 would seem a more realistic alternate choice there. I was admittedly also thinking in comparison to the R-2600 powered P-36/P-40 derivative and the Corsair airframe being better suited to the engine in terms of existing dimensions, aerodynamics, and fuel capacity. (and potential external load carrying capacity)
I guess there's still probably more useful places for R-2600s at the time though, at least if you assume both A-20s, B-25s, A-31s, SB2As, and SB2Cs are all more effective bombers and attack aircraft all around than R-2600 powered Corsair derivatives in their respective roles. (or, rather in the SB2A's case, just better allotted to one of those other R-2600 powered aircraft ... likely the same for the A-31, and also admittedly some of those used older engines before the Corsair would likely see service -or be more crippled by the 1600 hp limitation- ... or wilder ideas like trying to cram those 1939/40 vintage R-2600s into F4F or P-36 airframes)
I suppose the P-36 airframe mated to an R-2600 might make a semi-decent early war fighter-bomber in the sense the Jabo Fw 190s later did, but it really seems like the size and capacity of the F4U (and dive bombing capability) would make more sense in the attack role. (other than that, it's just the existing R-2600 powered bombers that would be better for those roles ... the question was more whether the F4U might manage better than SOME of those as well as SOME roles the Allison powered P-40 performed historically while possibly being a bit faster flying/climbing/turning/rolling than the existing P-40E)