Okay, some good ideas there.
Thirty years ago when Mt. Helens blew, cars were a little bit different than the ones these days: fewer computer parts, mostly still carburators rather than fuel injection, I think, etc.
A man I talked with was caught on the east side of the Cascades when the mountain gave its big blast, and he said when the ash started falling, he had to stop very frequently (every 2 minutes or every 2 miles, I forget which), take the cover off the air filter, remove the filter and beat it mostly free of ash. So, no matter what the eventual results were to the engine, the first and biggest problem was the air filter.
The falling ash was only half the problem; the ash that did fall was so light that any motion (walking or driving) would stir it up and mix it into the fresh falling ash, so the ash was coming from all directions. The air was so thick with it that while you could see headlights when they were relatively close, you still couldn't see the vehicle they were in. I've seen the photos of that, glowing orbs of light in very thick, heavy, dark fog.
Art, a couple of questions regarding what appears to be your very good idea...
Is there enough air actually moving through the engine compartment to clean the boxy pre-filter?
Would it be any better to have more than one side of the box open (covered with the filter material)? Even a wire frame instead of a box, covered with a filter? Would a fiber air conditioner filter work, wrapped around the box or frame? I wonder how many layers of pantyhose* could be used before it interfered with air volume?
Yuccahead's figures on air requirements for an engine would indicate that any filter material would have to allow enough air, fast enough, or the effects of a thick filter would have about the same results as a filter choked with ash.
Any more thoughts, keep 'em coming!
*Pantyhose, almost as many uses as duct tape!
Sue