Purely because of the nature of the problems that are posted, I'm not actually sure how a simulation algorithm can be used to put forth a solution, but if you can find a question where such an approach properly answers the question, I don't see any reason why you can't.
There's nothing inherent about simulation algorithms that automatically makes it not suitable for the site at all.
That being said, it may not be as helpful as an "analytical answer" if the latter is what the question asker looks for, and can suffer if someone requires a "normal" proof.
Short answer: There's no inherent problem that I know of, but it may not necessarily help others as much.
However, I also can't help but also address the first part that you've mentioned, even if that's not the main question you were asking:
To explain my situation with math as a form of context to the
question. I have a college education, which enables me to understand
some of the whole range of subjects treated here at Math SE. However,
I haven't used any hard math in the past years (my line of work
doesn't usually call for it).
I sometimes come across some questions that I can solve, albeit with
some difficulty (and probably with some errors), using the math I
learned (and remember)...
I'm in a similar boat (the only real difference is that I graduated more recently), and also find myself somewhat limited in the questions I can answer (the "limited in the questions I can answer" bit actually applies for me on the other Stack Exchange sites as well).
The main thing is that there's nothing wrong with being only able to answer a small portion of the questions. Sure, you may not be able to become one of the top users on the site, but you still can fill your own niche and be a useful member of the community. Your savvy with simulation algorithms sounds like something that could fill a niche just fine.