Yes, they can bite, but it's not likely to hurt. Their mouths are too small to damage human skin.
They may be able to hurt reptiles and amphibians with thin or delicate skin. You may see your pet flinch if they get bitten. If you're concerned, you can crush or remove the superworms' heads before feeding them to your pet.
However, superworms generally don't do significant damage — crickets have a worse bite. The belief that superworms can chew their way out of a reptile or amphibian's stomach is a myth.