Hi, f4mnect, hope your first time out with your trailer is a great success.
To answer your question, yes you can do that. The lifting motor for the top gets its power directly from the battery, so the 120 Volt shore power to the converter battery output will have very little effect. It won't damage anything to raise or lower the top while connected to shore power. It's not like raising the top while connected to the tow vehicle's battery charging circuit.
If the trailer battery is weak, and the tow vehicle is charging it, raising the top can pull more than 30 Amps through the tow vehicle's charging circuit, and this will blow the fuse in the tow vehicle.
However, the shore power converter in the trailer limits the charging current to the battery. The converter WILL help a very slightly weak battery raise the top, but if the battery is discharged, then the converter will not do the job.
However, I think it's more logical to have the top raised before you plug into shore power. It makes getting the power cord out easier, if nothing else.
- Jack