axeman,
The key to doing the types of random data testing you are thinking about is to do lots of them. You need a significant sample size to draw any useful conclusions.
Many traders pick a preferred method of trading (breakout, trend following, momentum, contrarian, scalp, whatever) and utilize filters and try to fit the market to their system.
Other traders will adaptive will try to fit their system to the market by asking the question: is the market currently trending or in trading range? Breakout, trend-following, LBR grail trades, etc. work best with trends; while oscillator/cyclic methods work best during in trading ranges; etc. These traders modify their methods (whether system or discretionary) to market conditions.
Now why not take that one step further? Instead of just asking "is the market trending or in trading range" why not also ask "does current price action show behavior closer to random or persistence". Based on the answer to this question you can shift your trading strategies. And I don't just mean entry-and-exit signals, but how about position sizing/risk? When markets show higher propensity for random fluctuations, either don't trade at all or trade less size. When price action shows clear non-random behavior the odds are much higher that your edge can exist.
The accuracy of measuring the degree of randomness is the tricky part. You have a measurement problem in that the more accurate your measurement the more time has elapsed and the more likely that the underlying behavior has shifted. This is the nature of the problem/challenge.
I'll conclude by saying a small edge is all you need!