The risks mainly are increased sensitivity of the teeth (mostly to
cold, but possibly to touch or heat as well) which usually resolves in a
few days to a week or so.  The bleaching solutions can also be
irritating to the gums.
    About the product you linked to: I see nothing wrong with the
ingredients.  It just seems to me that the bleach won't be in contact
with the teeth long enough to be effective.  And as far as using an
abrasive, this could potentially increase sensitivity.  Better to have
your dentist polish your teeth before you try a bleaching agent.

Steve