To what end? Want a dyed anodize finish or something? Would paint not give a suitable effect?
The anodizing bath is basically sulfuric acid solution, battery acid. It will dissolve tin and iron. It will passivate lead (leaded solder, I'm not sure), leaving a dull finish. It will do very little to copper.
Tin and lead of course are commonly used in solder, lead less so these days. (If this is for a special installation rather than commercial use, and you find lead greatly improves the results, perhaps you can get an exemption or something?) Iron often for component leads, and copper for component leads, PCB traces, etc.
If the circuit is isolated from the backing panel (usually the case I think, for LED PCBs?), then it can be anodized independently of that, and any corrosion of the circuit can be treated as a separate issue. If they share connections however, the circuit will be eaten away rapidly. A shared ground is often a good idea for electrical performance (particularly EMC), but keeping that separate for this step would be a good idea.
Anodizing applies a positive voltage to the work, typically 30V or so (up to a few hundred for hard anodize, I think); this rapidly oxidizes the aluminum, forming an insulating layer. Anything that dissolves in solution, will conduct strongly, while being eroded in proportion to charge passed.
If the board can be adequately masked, and rinsed and neutralized afterwards, it should be okay; mind that any acid residue on the board will lead to corrosion. If not, it might still be okay -- if the dissolution rate is low enough, and no electrical connection is made to the circuit -- or it can be grounded -- it might be doable before damage is done.
It might also work if the circuit is grounded (connected to the cathode), in which case some anodizing current can return through the circuit, which shouldn't have much effect (if the circuit is just power LEDs, they can handle some amperes -- some LEDs might light up in the process, but that should just be... something cute that happens, not actually a problem?). I would definitely avoid this if there's any active circuitry on there (i.e., transistors, ICs, etc. -- anything other than LEDs and resistors basically). Corrosion is suppressed or eliminated at the cathode -- hydrogen bubbles are given off instead -- so this may be a viable option.
Hmm... even so, there's no guarantee that any of the components are suitable for that environment. Some plastics decompose under low pH conditions, for example. I'd guess most things used for components would be okay with that (e.g., epoxy, silicone, vinyl), but it's hard to say for sure, and again, anywhere some can get trapped, it's not great for longevity.
And hey, it's not like LED panels are the most expensive thing -- try it and see. Mind that anything dissolving, may affect the quality of the bath; you might not get permission at a commercial plating shop, but if you have the capability of handling the chemicals yourself (the most toxic/hazardous thing is the acid itself, and it's just a strong acid, not nasty in any particular way), you could give it a try.
The worst that can happen, of course, the components just melt and fall off; the second worst, I think, is enough solder dissolves to undermine the components, and leave a frosty, perhaps oxidized as well, finish -- a porous surface that also traps acid, despite your best efforts to neutralize it. So it works but ends up failing some weeks/months/years later. This also might not be insurmountable, for example baking to remove possible trapped moisture, then running another soldering (reflow) cycle -- this time just with a thin coating of rosin (flux) on everything, so the solder melts and draws into a nice clean surface once again. That would eliminate or at least reduce porosity or oxidation that might be trapping acids. The subsequent washing step also helps clean out anything else that might be trapped.
Or there's the flip side: anodize first, then solder. If the dye holds up under soldering temperatures, this should be fine. The flat board surface should be easier to mask, and even if acid touches it, it might not be a problem -- ENIG might hold up without masking at all, tin plate may end up frosted or dissolved (leaving bare copper), and either way the surface should still be solderable, maybe needing a more active flux to get it back in good condition. Which would be a bit of a PITA for paste reflow, but maybe not insurmountable. Or like, if it ends up etched down to bare copper, maybe it could take a dip in another plating line to restore that (electroless tin plate).
So, hah, it might well be the best surface is bare copper -- usually given as OSP (organic solderability preservative). Shelf life wouldn't be great, you'll want to send them to the electronics assembly line within some months probably; but there's no plating or components to worry about.
Tim