The VFD is similar to a CRT with respect to burn-in.

Any stationary image, regardless of brightness, has the potential to create burn-in. The dimmer the image, the longer it takes.

The term "burn-in" is actually a bit of a misnomer. The correct term should be something more like "uneven aging of the pixels". This is the same whether it's a VFD or a CRT. The more a given pixel is lit, then the faster it will "age" and the dimmer it will be. So if you have some pixels lit all of the time and other pixels not lit at all, the lit pixels will age quicker and will appear dimmer relative to the other pixels.

The good news is that burn-in, even when it happens, isn't very noticeable on the empeg display.

One way you could work around this is to create a small set of favorite visuals which includes the VU meter along with a couple of other visuals. Then tell the player to auto-change between the different visuals. Then the VU meter would only be up a fraction of the time but you'd still get to see it.