If the panels supply 2000 watts of power, the battery will make up.
If you’re saying the max the panels and batteries can supply together is 2000 watts, that voltage will start to drop, and amps will start to rise, which going from 14.6 to 10.5 can by about a 30% increase in amps for these same power which can be wire overheating or ampacity in wires. My inverter has a fixed 10.5 VDC low voltage cutoff, so that would be tested. I would say taxing the inverter like that on a constant basis would be bad.
I don’t want to test my inverter at its limits after watching one of many YouTube videos of inverters bursting into flames when ran at their published limits. Those videos made me buy a UL458 rated inverter.