I think that depends on the company. I'd say, especially in the software industry, that if a company rejects you simply because you don't have a traditional resume, then they probably aren't looking for exceptional people.
A "traditional" resume is simply a track record in a concise format. If you're exceptional enough to not need one the company will probably be approaching you. If you're too pretentious to bother making one because you think you're exceptional I would expect it to be rejected.
