Soaking the snake helps relieve the itch and will drown any hatched mites on the snake, so yes definitely do it, but add the BlackKnight or other product as recommended by your vet. You have to treat the cage as well as the snake because mites, like fleas, leave eggs behind that will hatch and re-start the process.

If you can't get BlackKnight, clear the cage of everything and soak it in a weak bleach solution (1:10 or 1:20 bleach to water). Soak the snake's hide boxes in the same solution unless they're cardboard, in which case throw them away and make new ones. Clean the water dishes as normal. Rinse everything bleached thoroughly (3 times -- you don't want bleach fumes left), put in paper towels for substrate so you can see any mites or eggs, and don't put anything in the cage but water dishes and hides (no wood, no foliage, etc.). Put the snake back in, soak snake daily for half an hour to an hour, and repeat cage cleaning once a week for two to three weeks.

I've just dealt with a case of mites and they are a definite pain in the @ss. Good luck to you.