>> Is there any problem with plugging power in and bypassing the inverter.
You might try bypassing the inverter and
THEN plugging in the power
You should be fine. You are simply bypassing the inverter's transfer switch. I did this for a few days when I was experiencing inverter faults.
You will still need to charge the batteries, so you will need to keep the inverter's AC inputs connected to power.
You probably have a Magnum inverter. They have a number of fuses and resets that could be involved. A call to magnum could be helpful.