My only experience playing in random matchups was in a wifi tournament. My team did somewhat well, despite being story mode pokemon. I imagine that, outside of a tournament, that things are less serious.
Thing is, a majority of uber-competitive players won't waste their time with random matchups because they don't want to get stuck facing against casual players. But it really depends on how balanced your story mode team was. I've seen people use things like HM Cut in random matchups... but I imagine those types of story mode teams will have a hard time.
Because I can't say for certain how good your story mode team or strategies are, it's best for you to try it out.
