I know I have a couple of spiders living amongst my Orchids. I looked "mine" up some years ago, I think they are Phiddipus audax, a cute little jumping spider. As long as they stay in the greenhouse, I ignore the occasional little fellow getting a sunbath on top of an Orchid in the middle of Winter.
And so far they stay put.
I wonder if they would really make a dent into a happy bug population, but surely they eat one here and there.