The simple answer to this question would be no. Moss is a type of plant that is quite different from your regular garden variety weeds. The physiology of moss renders most weed killers ineffective. Besides, many weed killers also consider grass to be a weed.
So, if you want to keep the grass on your lawn healthy and green, conventional weed killers are out of the question. Moss killers are manufactured so that they only target moss or other similar types of plants while leaving grass and other plants intact.