I don't know the answer, because I can't identify the material. Both wet and dry types exist. The urethane foam type is used dampened with engine oil. The issue is whether putting oil on it would cause the fibers to cling together, thus flattening the filter into an airtight object, the way a wet dog's fur contracts and lays flat. Foam does not contract in this way, and is used slightly dampened with oil.
If your filter is now clean, it will not interfere with you starting and running the engine.
