That lines up with my experience. The alternating esotropia means that at any time one of my eyes acts as dominant, but it will change based on which direction I look and is also under voluntary control.

I have played ultimate frisbee for years quite successfully, and people were usually surprised when I mentioned I have no depth perception. I've met another A.E. person who was a good softball player. The hard part is when I have to look up at blue sky to catch something; the size difference between "can jump to catch it and cannot" is not very big, and there are no parallax/overlapping cues to draw on.

Interestingly, one friend said "Oh, that explains it" when he learned about my eyes. He noticed that I never look into a cup or glass straight-on when filling it, but instead look at it from the side so I can see how full it is. The growth of the circle of the top-of-liquid is small enough that I will heavily underfill a glass rather than risk spilling. As you suggest, it's not deep life-changing stuff, but it is quite a novelty!