Too subjective of a question. Low tier schools do place people in competitive specialties if that's what you're asking and as an average allo student you can still match into competitive residencies like anesthesiology, radiology, general surgery etc.
It comes down to what your goals are. For instance, getting into a great Derm or Plastics position would help a lot if you had a department in your home institution. It may also be easier to get research and finally the name brand matters for the elite programs in even primary care positions like peds, IM etc and your stats may not overcome the stigma of a low tier or state school (peruse the IM board for some examples).
If you're ok with university programs or just getting into a competitive residency, like ortho, no matter what program it is then you should be ok assuming you put in the right amount of work.