I have not used this. I have used a different type of "no peep" that I liked. However, I am not sure this will help your cross eye thing as it looks like it would still have to be seen by your brain with your right eye as your left eye being dominant will look across the sight line of the nopeep pin and be just as bad as not having it there.

It may have enough lateral play to move sideways enough to line up with your left eye and the sight pin. It seems like you would need to have one in hand or on your bow to know for sure though and since this seems to be a newer item, you might have to bite the bullet and be the HuntWa guinea pig.
This cross dominant thing is a pain as even though I do not have it, I have had to work with my ex who did as well as my son. For my son, he is young enough that we have been shooting both lefty and righty so he will be comfortable going back and forth with a gun, and have shot a bit lefty with a bow.