Would it make much of a difference if we played with the black square in the bottom right corner?

Thoughts or facts on this please.

Not really. Just most chess players prefer to have the board in the standard position because they have the starting positions with light and dark squares pretty much memorized. In an official FIDE tournament it turns out that the pieces were set up correctly, but the board was rotated the game stays the same and is transferred to a correct board. If there is an error in the starting position though, the game starts over.

"The lack of a brain helps my skull think better." - oinquarki

Hey thank you for that. Ive just often wondered if it would be different..