That would be the wrong thing to do, since, as you say, when they are dry, nothing sticks to them.
My thought was it's not actively sucking all the time like your air filter is, except in the times when you stall and its sucks back for a second (according to Yamaha it doesn't suck at all) in which case it would just be there to stop debrie from mechanically bouncing around and falling into the hose. Just curious what other people are doing. At the moment probably 99.9% of them out there have the breather hose totally open and exposed as they come stock with surprisingly few issues. According to yamaha to get the amount of sand in there that I had I would have had to pull the hose up and pour sand down it with the engine off. They're not oiled when used in a car but I don't really know what they do there either and it's a much cleaner environment. It's not really a foam material in mine, more of a cotton batting and thought oil might gum it up to the point of no air going either way. Probably cut up an older air filter into the same shape and have a zip lock baggy full of oiled foam pieces and change with airfilter changes. Thanks.