If you know you will utilize it, then yes it can save you money on repairs. Our house purchase negotiations came down to a busted water heater, and thankfully the homeowner had purchased a home warranty, so we could get that covered.
But, understand that warranty repairs will use equipment that is specified by the warranty company, not what you would buy. So, you will get an 80% efficient furnace (if your state allows them) instead of a 96% efficient one. Likewise, other appliances will be on the lower end of capability / quality, so if that would bug you, it might be worth it to bite the bullet. If money is tight, it can get you by, put start saving up for the replacements.
The water heater, for example, is a Rheem, which is notorious for having the heating elements fail. Having had this happen twice in three years, our plumbers finally talked the Rheem warranty department to use a different model's more-reliable heating element in ours. So far, so good.