That's exactly what I did and I bitterly regretted it.
Look up this article from PC Magazine sometime: "The Great American Phone Insurance Rip-Off."
When my iPhone's screen shattered, I took it into the Verizon store and they said, "oh, no problem! You have insurance, so all you need to do is call this number and they will fix the screen for $49."
So I called the insurance (Asurion) and filed a claim. The accepted the claim and sent me an all-automated, online form on which the only option was to pay $200 deductible and get a new phone. I called back and the rep said, "Nope, you're not eligible to get your screen repaired. This is your only option."
Mind you, I could buy the exact same phone in great condition for 300 bucks on eBay.
Fuming, I went back to the Verizon store to tell them that 1) they had never told me there was a deductible on my insurance, and 2) that their promise of getting the screen fixed for 50 bucks was inaccurate. I said to him, "Between the installments to pay the phone off, the insurance payments I've made over the two years I've had the phone and the deductible, do you realize that this phone (iPhone 6 Plus) would have cost me $1,024 all in all? If someone came to you and offered you an iPhone 6 Plus for over a grand, would you consider that a fair deal?"
The rep just gave me a look of faked sympathy, said, "No, that would be a horrible deal, but there is nothing we can do for you."
Phone insurance is a scam. I will never get it again, and invest in a good case instead.