Friend of mine just applied with UK passport and some UK pre-clearance code he obtained separately beforehand.

His app was straightforward with nothing notable to declare and a reasonably tame travel history.

Sunday March 19 Created GOES account and submitted app
Monday March 20 Amex charge posted.
Wednesday March 22 Amex GE Benefit refund posts
Tuesday March 28 Conditional Approval

9 Calendar days start to finish. He booked himself into IAH Terminal E for his trip next month and is pretty excited to get GE. He flies in and out of MIA often and GE can make a difference of 90 mins there.