The answer is no you would never depart with the altitude preselect at 0. You would normally set the initial level off altitude provided in your departure clearance, or an initial level off altitude indicated in the SID, or you might set a level off altitude that you have decided to use as a level off for the single engine profile in the event of engine failure, based on the terrain around the airport. All would be at least a 1000 ft above the airport at minimum.
You dial up that altitude in the AP's altitude preselect window, usually during the configuration setup during or after the crew departure briefing. When you are airborne, you will normally select the autopilot's speed hold mode (on the -8 AP it's called IAS mode) which makes the flight director command a pitch attitude to hold bug speed, then when you pass 400 feet or above, you engage A/P in IAS mode and it will pitch the plane to hold the bug speed you select during the departure. In IAS mode, whether you climb or descend depends on the power setting, so when you are climbing and descending in IAS mode you regulate the climb/descent with power while the AP pitches to hold the speed. You can also use VS mode, or vertical speed mode, and the AP will now pitch to a preset vertical climb or descent rate.
With those two vertical modes, the incident description doesn't make a lot of sense as they would have had to have selected VS mode and dialed in a descent rate, or been in IAS mode and cut the power. However...
The -8 400 has coupled VNAV, which adds an extra wrinkle. With VNAV engaged, the autopilot will pitch to climb or descend to an altitude preselect independently of IAS or VS mode, instead of just hold an airspeed or vertical speed, until a preselect altitude is captured. Coupled VNAV can also follow step climbs in a SID or step descents in a STAR if that is programmed into the FMS.
So my guess here is that they forgot to set the altitude preselect for their planned departure level off altitude, then engaged the autopilot in VNAV mode during the climbout, which caused the plane to dive to the existing altitude preselect of 0 feet, upon which hilarity ensued.