Yes, it could make a significant difference. You will now be clearly entitled to use the VWP (technically, the VWP requires you to have a "return ticket" but that interpretation is often loosely applied to include separate tickets) without relying on oversight. You will also be demonstrate temporary residence in Mexico and intent to return to your country of citizenship, thus creating a tie to the UK that was not hitherto in place. Taken together, these create a far lower risk scenario than otherwise.

Remember, the main thing is to not attract attention to begin with. Once they start poking around in secondary, it is a toss up whether the officer woke up on the right side of the bed that morning.