At least two HP OfficeJet models come with a driver CD that includes a hidden installation of Growl. Specifically, the “HP Message Center”, which is responsible for claiming that your printer is out of ink, uses Growl to do it.
As far as we are aware, removing Growl does not break these drivers' ability to print or scan, though we cannot guarantee that. If it does, that is a fault in HP's drivers; Growl does nothing that a printer driver should be unable to work without.
As Growl is installed by HP's installer, only installing the driver will cause Growl to be reinstalled; it should not suddenly reappear at restart as with Dropbox. However, this may extend to driver updates you download from HP's website. We recommend using the printer driver updates from Apple.