I know the feeling when you pooch it.
To answer your question, yes, you can just move the SD card to a new unit. You will need to go through the initial step of commissioning the WiFi of the new unit as the WiFi configuration is not stored on the SDcard, but once connected, it should just continue where the old unit left off.
But first, lets talk about the old unit. Those AC jacks can be problematic. Traditionally connectors like that were thru-hole soldered and had a lot of mechanical integrity. IoTaWatt uses surface mount connectors. They have plastic pins that register in holes in the PCB to provide great sheer strength, but the four solder pads don’t really provide the same lifting strength that thru-hole did. Also, the pads are large and sometimes don’t reflow that well.
If the connector came off but didn’t rip the solder pads off the board, you should be able to just solder it back on.
That’s one solution. Another is if you have a V5 unit and not using all of the inputs, or can sacrifice one, you can use one of the three-phase voltage inputs on inputs 13 or 14. Just configure it as a VT, connect your AC adapter, and then go through your inputs changing the voltage reference to the new VT.