Would spiders (and mites) be harmful to a compost system?

I have several large (14” diameter) containers in which I found an infestation of spiders and mites. I was able to save four of the plants, but there were another four in which the plants had died. The surviving plants have now been cleansed of the infestation, but I have a large amount of potting soil, which I am afraid might be still infested. I currently have it segregated from other pots and garden soils.

If I introduce this infested soil into my compost system, will there be detrimental effects, or will the spiders follow their natural course and find elsewhere to go?