A few separate points:
1. The question is still open: on the avionics in question, can you have active guidance modes with the FD hidden from view? Because my mind boggles at trying to imagine anyone - at any point along the automation dependency spectrum - merrily flying along in an initial climb with a visible FD commanding a pitch into the ground, and then engaging the AP in this state.
2. Prior to engaging the AP, if they were climbing with a visible FD pointing at the ground, I can easily imagine this (unfortunately). One of the aspects of the automation dependent culture is a taboo against not having the FD up, even if it's 100% inappropriate. I remember a sim session where we did a PRM breakout, and in the 90 degree turn away from the airport, (I was PF) I was turning against the FD, which was still commanding a turn back onto the localizer; and the PM was talking on the radio so I couldn't ask him to set it to heading and set the bug. So the FD at that point was counterproductive (i.e., worse than useless) so I reached up and turned it off to avoid the distraction. I got scolded for doing this. Yes, in the instructor's absurd conception, it was better in the interim to have it up and pointing the wrong way than to turn it off. "All available resources," right?
(Imagine explaining this scenario to the inventor of the FD.) So if this crew had gotten flogged in the past by instructors in a culture like this, I can certainly see how if they bungled the settings before takeoff, they would have felt more comfortable having a wrong-pointing FD than not having one.
3. Once they engaged the AP and were in (ahem) "plummet" mode, I wonder if they spent those 15 seconds distracted away from noticing the plummet, or were in the often-fatal "what's it doing now" conversation.