It's a widely held myth that this might have tipped the balance and enabled a LW victory, but it would have made little difference to the outcome, to be honest. The Germans lost because of an overestimation of how well they were doing and an inability to continue because they were not able to replace their losses as fast as Fighter Command could replace theirs. German intelligence was faulty and never really gave them an accurate picture of how they were doing at destroying RAF aircraft and airfields, so they miscalculated when to begin attacking London. Sure, more RAF fighters might have been shot down, but the German heads overestimating their successes wouldn't have changed even with longer-ranged Bf 109s.
By the end of October 1940, the RAF had more fighters than they began the battle with, but the LW had not been able to recuperate their increasing losses to the same degree - they had to replace fighters, bombers, recon aircraft, long-range fighters, and dive bombers and their aircrews, whereas the Brits only had to replace fighters and their pilots. It was a battle of attrition the LW were losing at and having longer-ranged fighters wouldn't have changed that at all. British tactics also nullified the advantages the German fighters had over the British ones, largely their superior numbers and superior altitude. Stats show that Bf 109s shot down more RAF fighters than RAF fighters shot down Bf 109s, but the LW lost a larger number of aircraft all up than the British did. The Brits achieved a higher kill to loss ratio compared to the LW.