You passport, even linked to GE, does not control access to TSA Pre Check.

TSA Pre Check selection marked on your boarding pass does. Your Known Traveler Number you got with Global Entry, not your passport number, must be linked to your airline reservation to enable selection for Pre Check. Even having a KTN linked to your reservation does not guarantee selection for Pre Check, it just increases the odds of such selection, though by quite a margin.

It also has nothing whatsoever with departing the US. Pre Check is part of the overall air travel security regimen that applies to all flights originating in the US, domestic or international. It has nothing to do with immigration/emigration.

Enter your GE PassID/KTN on your reservation and you probably will be selected for Pre Check. But maybe not.