It really depends how good he is as a boxer. Boxing fans are a lot less forgiving and quick to write guys off after losses, especially in the UK.
Assuming McGregor follows the same trajectory, he's making a name for himself 2013-2014 and fights for the title in 2015... he's fighting at 147-154 in boxing, and that puts him in line to fight guys like Pacquaio, Mayweather, Canelo, and some other huge names. So there's a ton of potential there.
So lets assume the alternative universe plays out the way it does in reality. Conor fights Aldo in late 2015 for the 145lb title. Who is the #1 147lb boxer in the world in late 2015? Floyd Mayweather. So McGregor beats Floyd Mayweather by early knockout. He gets upset by a highly ranked fighter in his next fight, then avenges the loss, and then challenges Alvarez for the 155lb title. Assume that happens in boxing universe too. Who's the #1 154lb boxer in the world at that time? Canelo Alvarez.
So yeah, if McGregor knocks out Mayweather and Canelo Alvarez, he is a bigger star than legitimate Conor. I think people would be praying to his statue all over Europe.