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