Unlike most of the reviewers my story had quite the happy ending. I am a new homeowner and the one year HSA warranty came along with the house which was paid by the seller.
About 6 months after we bought the house - our bryant furnace of 29 years old started acting up and completely stopped working in the midst of the freezing pittsburgh winter. So I called a local heating guy hoping it will be a quick fix or a simple cleaning up but unfortunately it needed to be replaced. We got an estimate from the local guy and few others the same day which averaged around $3000 to replace with a 90%+ efficiency furnace.
Since furnace/AC was supposedly an optional upgrade to the warranty - I called HSA to see if the furnace was covered under the warranty and to my surprise it was. However, they will have to send their own heating contractor/provider to check and see if it should be be fixed or replaced. Few minutes later - I received a call from their Heating Contractor (Main Street Mechanical) to set up a schedule which I set it up for next day since I was at work and also the fact that the weather was starting to warm up (Around 40 degree - Yep! that's the pittsburgh's version of Warming Up)
The next day - MSM (Main Street Mechanical) came - took apart the furnace and said it had to be replaced and that the Home Warranty would replace with a new lennox furnace that will be similar to what we had in terms of BTU/stage/efficiency. However, I could choose to upgrade to higher efficiency but will need to pay the difference out of my pocket. Also, there's an option of cash payout in case we prefer to go with a different contractor. FYI! the warranty only covers the equipment and not the labor/duct work/and some other misc. that goes along when replacing the furnace. But don't worry - they will give you an exact breakdown of everything that's not covered under the warranty.
So, after going back and forth with HSA on the exact details of the equipment - it was a lot cheaper for us to not take the "cash out" and just go with HSA and MSM to replace the furnace. And we decided to go with the upgrade and ended up paying only around $1200 for a brand new lennox 93% efficiency.
With this experience in mind - I would definitely recommend having some kind of home warranty. It will at least help you half way through.