It's probably safe, but they may not eat it.
Just FYI, buying hay in small packages from places like Walmart and pet stores pretty much guarantees that you get the oldest, driest, most expensive hay on the planet. You can usually get much fresher hay from an online supplier like Small Pet Select or American Pet Diner for about 1/3 to 1/4 of the cost, per pound, of hay from places like Walmart. You do have to buy it in bulk, but it's still way cheaper.
Still cheaper is hay from a local farmer if you live in an area where you can get it. A bale of hay weighing 30-50 pounds will usually cost around $20. Even if you have no place to store it all, you could throw lots of it away and still come out ahead.