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For example, I'll put in my 100 trades that took place over a month's time, and let it run over 10,000 simulations. That's,

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The purpose of the MC simulation is to see possible outcomes and Drawdowns given that the future of your system follows the same cumulative frequency distribution your past trades has. It means that your system has to be stationary in a mathematical sense.

A first step after back testing is to do forward walking testing and do same MC on this. Then you can use real trades and see if the system is broken and should be stopped.

Its all math analysis of the system you use.

If you change system or break its rules any MC analysis is of course meaningless.

Let me have a crack at this question both the OP talking about draw downs growing at a rate of SQRT(N) and then Monte Carlo methods and stationary of the series.

First off if draw downs grow at a rate of sqrt(N) then all HFTs would be bankrupt by now because they would execute millions of trades in which case they would easily approach ruin, sqrt(N) actually accelerates pretty fast so these firms would have blown up within a matter of days. As we can disprove it with this single counter factual, draw downs do not model in this way.

Monte Carlo is not used to see if a time series is stationary, you would use Augmented Dickey Fuller or Engel Grainger 2 step. MC is a method that allows you to resample/boot strap a larger distribution given a limited number of samples, this will allow you to hopefully approach the true distribution of which your samples come from and get better confidence intervals. However garbage in / garbage out, if your trade samples do not come from the true distribution, you can sample it all you want and the answers are meaningless.

You can use several methods to determine if a system should be stopped. Although I am an advocate of MC, it is not how i determine if my system should be stopped. The MC may help me generate the CI's or medians, but I use statistical process control methods for the actual monitoring and alerts.