The V-1710 did have problems with engine's intake (ie. between supercharger and pistons), where the fuel would cease to be 'atomized', and started to revert into fluid as it was before exiting carburetor nozzles. Low temperatures worsened the situation, ie. when aircraft was flying high, and proper intercooler was used (as in P-38J/L, and the P-38J was seriously plagued with the problem, especially if low boost was used). The solution was to insert a venturi pipe in the intake duct, so the air stream was sucking any of the fuel from the bottom of the duct and re-atomize it. That way V-1710 also got rid with backfire screens (wire mesh, located just before the pistons), thus gaining 1000 ft in full throttle altitude (single stage engines, eg. installed in late P-39Qs) or 1500 ft (in P-38L).
On the opposite side, the earlier P-38s have had low-capacity intercoolers, and fuel in the duct didn't plagued them? The fuel injected there might've helped to cool the compressed air slightly better? They still have had the backfire screens, though, and these do lower the engine output.
So, after this lengthly intro - IMO, the direct injection would've improved the V-1710. We can take a look at the two stage V-1710 for the P-82 - those were without the screens, but backfired violently when pushed to the limits. The NAA installed backfire screens on their own, but GM (owner of Allison) was against that and managed to cancel the NAA's effort, employing political pressure. At the end of the day, the Allison engined P-38 have had slightly less performance vs. Merlin-engined ones. Edgar Shmued was very bitter on that GM's move.
On the opposite side, the earlier P-38s have had low-capacity intercoolers, and fuel in the duct didn't plagued them? The fuel injected there might've helped to cool the compressed air slightly better? They still have had the backfire screens, though, and these do lower the engine output.
So, after this lengthly intro - IMO, the direct injection would've improved the V-1710. We can take a look at the two stage V-1710 for the P-82 - those were without the screens, but backfired violently when pushed to the limits. The NAA installed backfire screens on their own, but GM (owner of Allison) was against that and managed to cancel the NAA's effort, employing political pressure. At the end of the day, the Allison engined P-38 have had slightly less performance vs. Merlin-engined ones. Edgar Shmued was very bitter on that GM's move.