This raises a question, though. When I uninstall through impulse, is there an "install count" being decremented somewhere?
No, it's just a matter of if Impulse installed it, Impulse needs to uninstall it. It's similar if you install something using InstallAware, for example, it'll use an InstallAware uninstaller; if you deleted all traces of InstallAware from your system, you'd find yourself unable to use the uninstall.
Add/Remove Programs in windows does not actually do anything itself, it's basically just an easy access list to the various uninstallers (whatever method they use) on your machine. So whether or not it's on the list, there's still an app (be it Impulse, InstallAware, etc) that needs to handle it and the uninstall can't be done without one.
