I've read so many horror stories about those home warranty programs, and it looks like they almost never pay out what you expect, and when they do, it's a huge fight and hassle, or they give you sub-par equipment. From what I've heard, your best bet is to negotiate as much of a cash settlement as you can get, and then take that money to put towards the new whatever you may need. It's never enough to cover a quality replacement.
The local realtors in our area are clearly in bed w/them. When I sold my house, I was "lucky" that the buyer requested I cover the first $500 of the warranty, because having pool equipment makes those plans at least $800.
My other neighbor sold a few weeks later, no pool, smaller house (one A/C system instead of the two I had), same spiel, same $500 credit.