probably not for you. If you had runflats, then I'd say yes. Runflats aren't supposed to be patched, in which case the warranty would get you a new tire. We actually patch run-flats anyway.
but with regular tires, nails or screws are most common and not a big deal. maybe if you ran over a chunk of metal and shredded the tire. but then a new tire would only be 150-200 maybe