The link between GE and PreCheck is softer than your message implies. Under PreCheck, a risk score is calculated at the time of check in for each trip you take on a participating airline and through a participating airport. You won't know if you're eligible for PreCheck (ie, expedited screening) until your boarding pass is scanned at the airport. You also have to set up a PreCheck profile with each airline that is participating. Entering your GE number (instead of your airline loyalty number) in your profile will likely significantly improve your odds of getting PreCheck for any trip, but it won't guarantee it. You can have GE and never experience PreCheck if you fly from small (non-participating) airports or if you travel internationally (since international itineraries are generally* not eligible for PreCheck).

*some exceptions have been reported. YMMV.