A social experiment. What is the worst that can happen?
I like to think I have a pretty vivid imagination, so the worst thing I can reasonably imagine happening is that you would be seen as trying to perform an experiment with human participants without proper controls, questionable experimental design, possibly a lack of appropriately rigorous analysis (if this isn't your specialty), and lack of ethical review and oversight. From an ethics perspective, you propose to use deception on uninformed participants while possibly obtaining personally identifiable information on them which could lead to them facing serious social consequences if they were identified. With the mob mentality of the viral internet as it is, the consequences could be pretty darn severe - up to loss of job, death threats, actual violence, and more. Sensitive topics require sensitive handling, which is what any functioning IRB and responsible researcher would insist on. 

In reporting on the results, even if informally on a blog, you could be seen as offering a pseudo-scientific view (or worse) on a controversial and important topic. If your experiment was performed poorly or your analysis done improperly, you could lend weight to an incorrect view - either providing what could be cited as evidence that discrimination does not exist where it does (thus making it harder for people discriminated against to make changes or be taken seriously), or supporting the view that discrimination does exist where it doesn't (leading to negative consequences for people who are doing nothing wrong and deflecting attention away from more pressing, extant issues). Bad science, even done with good intention, can easily make the world worse.

If some random blogger or journalist did this, most of us can gratingly dismiss it as "they don't know any better", or just the world of click-bait, etc. But if you were a qualified scientist who should know better, people might not be so willing to dismiss such activity just because it wasn't intended to be scientific and it wasn't intended for publication. Most people won't even know the difference in what is and isn't intended to be scientific when done by a scientist, and many that do know the difference might not consider it an excuse.

As Dawn pointed out in a comment, one version of this is called an audit study, and there is a pretty large body of literature that tries to do basically what you are suggesting in a systematic way. I cannot even try to count how many studies of this sort are published, but I'd be surprised if it wasn't already in the thousands, looking at everything from gender to race to the impact of varying lengths of time gaps on a resume. 

Finally, the nature of this sort of field study is that even with everything going your way they are hard to do correctly. No simple analysis method works even if you did everything right and collected all the data appropriately. There is too much randomness, too much heterogeneity, too much structure, to allow any simple bit of statistics to give the correct interpretation. In short, unless this is your specialty, it would be trivially easy to get everything else right and still come to exactly the wrong conclusion.

For those who are not familiar with this kind of statistics, a classic example of how a simple analysis can go wrong is Sex Bias in Graduate Admissions: Data from Berkeley. In a simple aggregate analysis, it looked quite clearly that women were being admitted at lower rates than men, and thus bias was quite obvious to the point that the deans of the school were concerned this could be the basis for a lawsuit. It turned out it was a nice example of Simpson's Paradox, as it turned out the cause for the difference was that women were more likely to apply to departments that were crowded and competitive and thus harder to get into for everyone, while men were more likely to apply to departments that were less competitive. 

If a similar condition existed in the employment sector, where you were applying to jobs in industry that turned out to vary in their selectivity in a way that you were not considering, this would mess up your analysis, and you cannot easily collect more information that would allow you to fix it. After all, I'm sure you weren't inclined to use random selection in your own employment search!

So, in summation, the worst that I could imagine happening is: you end up doing bad science that would reflect badly on you and would not be easily excused just because it wasn't intended for publication; you come to the wrong conclusions and in a way which could hurt innocent people; you casually report information that could be used in dangerous and damaging way; you end up being identified as the person responsible and it goes viral, so now the most famous thing you'll ever be known for was this thing you didn't intend as a serious study (and which could have gone horribly wrong); and, as a bonus, you could just end up wasting your time and the time of others for no benefit. 

And since its the worst thing that can happen, I suppose you could also end up with a headache. Things can always be worse by adding a headache.