I think so. Straw is a lot cheaper, but hay (alfalfa?) is a wonderful soil amendment. Both mat but straw less so. Layer it thick! Like at least two inches. You'll see there is a lot of air space until it gets wet and then it sort of collapses. But enough of it will supress weeds, just as well as leaves do. You will have some wheat sprouts from the seeds in the straw but it should be easy to pull out and lay down to add to the mulch. Or leave it! Hard to advise on that without being in the space and seeing the situation. (I tend to be lazy with the sprouts from straw mulch, myself.)
Good luck! And, sorry about your friend's heart attack, geeze.
Oops, Catmint, we cross posted. I've used straw and hay both as mulch many times. Works just fine.