It keeps running even if you're doing something else, you can get back to it via the Jobs page, and it's lifetime is extended, so you can get it's results for a longer time.
I can't say from experience, but I'd guess(!) if there's any, it's minimal.. just what is not used to have your GUI updated, but I'd say the actual search load is the same.
Hope that helps - if it does I'd be happy if you would upvote/accept this answer, so others could profit from it. 🙂