Furnace replacement through Home Warranty company?

I recently bought a house and I had someone come to do a tune-up on the furnace, which I believe is original and about 30 years old. Almost everything checked out but he thinks I have a split heat exchanger. He's suggesting I get a new unit. I'm wondering if I can sign up for a home warranty and after the waiting period file a claim. It looks like American home shield offers up to $5k for Hvac repair or replacement. Even if they repair it (which I hope they would just replace) i feel like the $500/yr fee and $100 deductible would be worth it. Anyone have any luck with something like this?