It seems to me that because part of the image the lens is passing to the sensor gets cropped due to sensor size that it would take more vignetting to reach the cropped sensor. Is that right and how much would this really be in practice? Is it 1.6x more attachments (which isn't a whole lot) or is there fancier math involved?
To actually work out a formula would be complicated as it depends on the focal length, but for most full frame lenses in order to vignette when used on an APS-C body, you would probably have to attach so many filters that vignetting would be the least of your worries!
The distance between the corners of a full frame and APS-C sensor is about 8mm. If each filter reduces the image circle by 1mm all round, you would need 8 filters to made their presence felt.