no...
see, you don't understand...
you don't need DC supply. you need frequency. so you need AC to get voltage transformed to high voltage. if you connect DC current to VFD, what you get? nothing. VFD changes frequency. and what is frequency of DC? 0. with tesla coil or whatever transformer, you need AC to get electricity converted (transformed) to other voltage. principle of the coil, whole magnetism and induction is that you have to have something what is moving to create magnetic flux (or whatever, I was not learning this on English...). either magnetic field (in transformers and motors) or moving parts (in generator). so in transformer, in primary you have AC at some frequency, magnetic field is oscillating within the core and there you get transformed voltage on secondary. in same frequency you have on primary.
DC was in game just for that toy I linked as that is designed like that. but you remember fast oscillating switch in that device? that was making frequency by cutting primary supply, although it was giving only upper part of the wave and it's squared (waveform of AC is sinusoidal and it's going equally on both sides, up and down), that is enough for rough device as is transformer
next... for making arc, you need high voltage. doesn't matter is AC or DC. high voltage DC will also make nice arc (and kill the rabbit). but we are using AC because it's easier and cheaper to get high voltage from low AC voltage through transformer.
so you understand now? a bit of theory
simple: if you want just arc between nails, find some old TV on garbage, take out HV transformer, connect secondary to nails, find correct distance (you can calculate everything taking in matter voltage and material use or start on some distance and simply get nails closer until you get arc). primary you connect to your house supply. this is very fast and efficient way to get yourself killed or your house burned down.
if you use vfd for changing frequency (and that's low frequency), you will just see your arc sparking slower or faster, nothing spectacular
check that sites I gave you for tesla coil, it's more interesting and you can build some amp with oscillator to play with
btw, that vc2002 what you are mentioning, is that this thing:
Aidetek: New VC2002 Function Generator 5 LED display 0.2Hz~2MHz
that can't produce arc. it's for testing and calibrating