I've tested Veronica's damage/armor with CHA 1 and CHA 10 via console commands.

I saw zero difference.

Does Companion Nerve bonuses via CHA actually do anything? Can anybody confirm?

I can confirm that there is a large difference between a 1 CHR and 10 CHR companion.

I know Veronica is bugged in some ways. Maybe its that or maybe Nerve doesn't react to the console cheat.

Veronica is bugged, yes.