It's fine for the shell, but for the liner it would require an enormous amount of rinsing to fully flush it out. Woolite on the other hand is much less viscous and rinses more easily/completely. Also, it's pretty darn gentle on your scalp, where SG can be aggravating.
Many helmet companies offer a true wash product for their liners. You could pick one of those up if in doubt. But Woolite is probably just as good and may be present in your home already.