It shouldn't do as essentially it isn't active, as the More Info (How it works) link says, it optimises the sqlite database files so they load quicker. It also suggests that you run SpeedyFoz every 1-2 weeks, which to me indicates that it isn't active.
How does it work?
Firefox uses SQLITE databases to store lots of its settings. By the time the databases grow and Firefox starts working slowly. SpeedyFox compacts those databases without loosing any data.
How often should I run SpeedyFox?
Depending on your browsing activity we recommend optimizing your profile once in 1-2 weeks.