I don't think that is a very likely scenario.Here is one sceanrio I can think of.
If for some reason, the power is failing at 6 AM (or earlier and coming back on at 6 AM), there is an initial inrush of current that occurrs when the capacitors are charging. This is a very fast rise because it is charging the capacitors almost instrantaneously. Many VFDs have various methods of mitigating that, i.e. charging resistors, DC bus chokes or using SCRs on the front-end instead of diodes, but some do not.
TBH, I have not come across any VFD that did not have a precharge circuit.
Inrush is one problem. But not the only one. Without the precharge, the step change in input voltage would result in capacitor overvoltage - you have simple LC circuit with a potential transient at twice steady state operating voltage.
Input line reactors or a DC choke are likely to exacerbate this, so won't mitigate that fundamental fundamental issue.
I don't think capacitor inrush is the problem.