I agree with I'mnoPrince.. but just from my experience of seeing the attraction with the lights on, it doesn't appear to go 'underground' in the sense that there is a tunnel or anything like that. The floor of the attraction might be 12-24 inches lower than the 'ground' level of MK exterior to the attraction but that's hardly what I would call a basement or 'underground'.
This map of the utilidor system seems to show the utilidors would go roughly underneath at least part of the Space Mountain structure but then its hard to say for sure.