I’d say no because it isn’t the same as long strands of hay, they are soft pieces of hay stuck together, they bite them with the front teeth and there probably isn’t much molar involvement in eating them in anywhere near the same way as strands of long coarse hay - so teeth overgrowth would be a potential problem.
if you’re struggling with allergies, have you tried different types of hay?
EDIT - the packaging for hay cookies makes it sound as if you can (although they can have their packaging say what they like) but I would be incredibly wary of using it as a replacement for loose hay. My rabbits (piggies don’t like them anymore) get a hay cookie once a week for a bit of variety and a bit of something to do.