Taking as a starting point that most education and credential-seeking is in fact signaling good traits to employers (rather than productivity enhancing) one has to wonder what sorts of strategies an informed job-seeker might use to take advantage of this system.
One aspect of signaling is that it has a negative externality on other job-seekers; every new degree I get makes others look comparatively worse, so they need more degrees and so on. It's an academic arms race. Only one person can be the "best" candidate, and as more and more degrees are acquired, the marginal value of each continues to fall.
So what about counter-signaling, i.e. intentionally refusing the signaling game or sending the opposite of a positive signal in order to distinguish oneself from others? This phenomenon certainly exists in some areas; think of brilliant Berkeley mathematicians who dress like homeless people. They're simply so good that they can actively disregard social convention, and the fact that they can afford to disregard convention is further evidence that they are that good.
So when might it be advantageous to do something outlandish when applying for a job, like submit a resume written in crayon? It would certainly stand out, but to work I think these other three conditions also have to be met:
1. Other observable traits already show you are highly competent;
2. The signaling market is fully saturated;
3.. Value placed on conformity is low.
What sort of jobs might fit these conditions? I think the third is least likely to be satisfied, because people in general (and employers especially) tend to value conformity. However, being a nonconformist in polite and non-threatening ways can sometimes pay off, as this intern's application to Wall Street which went viral demonstrates.
If you're a demonstrated mathematical genius applying for a hedge fund position along with 10,000 other mathematical geniuses, maybe a crayon resume would pay off. Unfortunately,I suspect for the rest of us the conformity test would lead that resume straight to the trash bin.