I can't speak to GE, but I do know when my DH and I went before Immigration for his green card they knew every time he'd entered the US on his UK passport and every date he'd been picked for secondary screening (he had a LOT of Saudi Arabian visas and residency permits in his passport, as did I in my last passport, and we used to get pulled all the time). They knew every time I'd been pulled, because they asked me about when I went to the UK and what I'd been asked about at reentry.

So somewhere a chunk of that information is recorded.