We had a Coleman popup for many years - not sure the Flagstaff is exactly the same, but with ours, nothing on the 12 volt side of the system - lights & lift motor - would run when the battery was completely dead. When plugged in the converter will charge the battery and power those things, but at least with ours, if the battery was dead they wouldn't run until it picked up a charge. Plus, there may be a safety device that doesn't let the converter run even when plugged in until the roof is up.
So, you would need 12 volt source from your tow vehicle or from another battery to provide the alternate power source to lift the roof. One thing to consider - the battery shouldn't have been dead when you arrived. One thing I learned the hard way is that many vehicles don't have the fuse and/or relay installed from the factory to power the pin on your 7 pin connector that charges the battery. With a 3 way fridge common on pop-ups, it can drain the battery while driving if the vehicle isn't sending power.
I would start with finding out why the battery went dead - probably an easier fix than an alternate power source.
Or, our method was a popup with a manual crank - and kids!
2005 F-150 FX4
2013 Rockwood Roo 23 IKSS