It is possible to have a filter prior to the velocity stack. The stock air filter on the Porsche 911/914-6 engine has a canister that fits around the top of the carb/velocity stacks.....and then a large air filter housing fits on top of the carbs. This provides both the performance advantages of a velocity stack - and the benefits of a filter....and it makes the intake weatherproof!
And for those who want something a bit lighter.....they do have aftermarket paper, gauze of foam filters that can fit over the velocity stacks.
And you can get them with rainshields that keep water from dropping into the filter.
Is this as efficient as an open velocity stack? Probably not - but it deals better with the dirty air and water that a street driven car or bike has to endure. Grit in the air can drastically shorten the life of the piston/rings/cylinder.