Ours get hay regularly, because we grow hay and have to buy straw, hay can be as cheap to use as bedding.
The pigs eat some, and love it, and lie on the rest.
However it is supplemental to feed not a substitute. Piglets will nose around and eat a few strands.
It does help firm up pig poo (roughage), making it easier to clean, for our expectant and new mums who are housed in the yard.
Used as bedding, hay can soak up water, unlike straw that acts as a barrier, so we use both, and don't use hay when wet pigs will be going into arks.