Brine Shrimp Direct does not recommend any contact of cysts, OR hatching water, with your tank water.
Artemia Reference Center says to hatch and rinse before using as food or growing out artemia.
Aquaculture companies hatch, rinse, and grow out.
Reason for this? Cysts can and sometimes do, harbour nasty bacteria that in worst case scenario, can wipe out the container it gets into.
Also, the cysts can get lodged in the digestive track of some fish, causing problems that might lead to death.