I can't truly say for sure, as soaps & detergents are not all the same, nor have I ever allowed my snakes to drink soapy water. As I said, I believe the most it would do is cause diarrhea, but for a snake already dehydrated from a mite infestation (that's why snakes die from mites...loss of blood > shock & organ failure, circulatory collapse) it compounds the dehydration, so I'd avoid letting a snake ingest any soapy water. Never put soap in their water bowl & leave them alone to drink it- soaks with soap are only with supervision.
It won't hurt her eyes...they're covered by a clear scale, remember? Their "eye caps" come off with each shed. But the reason you stay right with a snake soaking is to make sure they don't drink it, & because the water is never deeper than the snake's body height (so they aren't having to swim) & you want to make sure the snake stays in contact with the water as much as possible.
FYI, it only takes a drop or 2 at most of soap to drown mites- more than that is wasted. It only takes a tiny amount of soap to cut the surface tension of water, so the mites cannot stay afloat. That's why they drown- you don't need or want a bunch of bubbles in the water. And mild soap like Ivory or Dawn dish soap is preferred.
I've never used taurrus mites nor know of anyone who has, but I hope they work well for you.