"If we burn all the wood, then is it OK?" This sounds alright on the surface, but it isn't really the case. There's no way of knowing how far along in development (maturity) the insects are; they could emerge before the wood is burned.
This is the essence of a recent correspondence that Deborah Landeau, a Conservation Ecologist with the Maryland Chapter of The Nature Conservancy, had with some of the local leaders of a cub scout group. She's right, of course. You can't be too careful- maybe an insect will hatch out of the wood on that exact day that you unpack it out of the camper. In the case of microscopic fungi and viruses, it could simply blow away while you are stacking it to be burned that night, and you'd never know it.
One parent pointed out that she never buys wood, but collects it from her yard, in a county that's presumably EAB (Emerald Ash Borer) -free... We discussed how one can ever be sure EXACTLY how far the insect has spread.
It is a huge risk you'd be taking- despite seeming like a good idea. Pests spread to new areas, and despite all the best efforts, a new infestation could take months or years to get discovered. So even if your county says it is EAB-free, it could possibly have an undiagnosed problem.
You don't want to be the one responsible for spreading an invasive pest, no matter how unlikely it might seem at first. These are great questions, and they point to a good awareness of the issue.