No. It won't stop an active fermentation. Although it can definitely make the environment less than ideal for the yeast, so I wouldn't add it until the fermentation is done.
The intention of adding a sulfite it to protect the mead from oxygen, bacteria, and other things. It does this by binding to that stuff before it interacts with the mead. Again, not at all necessary, just an added layer of protection. With my meads I usually do a sulfite addition with the second racking (because that's handful of months in and I know the fermentation should be done), or any time I'm putting in an additive. Whether that be fruit or whatever.