I (unintentionally) had the trailer plugged in with the battery disconnect switch open, so kind of the same thing as not having the battery installed. Everything worked, and the converter supplied 12 volts to the lights and other 12V stuff.
The way I realized it was the slide motors were cutting out. The battery gives you a "buffer" for surges or higher draws. Once I closed the switch, the slides ran smooth again.
So, yes, you can plug in without the battery - not sure if there is any risk to doing it.
2005 F-150 FX4
2013 Rockwood Roo 23 IKSS