I find it does, although my hands are not really too big either.
I fit in between a standard and a midsize. Standards feel too skinny, and I can't really swing too hard with a mid size without excessive wrist movement. I have found that a standard grip with an additional wrap gets me in the right comfort zone.
Toying with the amount of wraps is probably a better barometer than simply hand size is. It's all about what is comfortable to you!