I've never done it, but you would assume that the object takes on the colour properties of the texture used - and the avi on a plain is only a glorified animated texture.
So, if the avi has a green background and you set that colour to be transparent for the plain, it too would be transparent.
But, I await being corrected!...
What springs to my mind is the compression codec you would have to use.
My first thoughts are that using something like XVid or DivX would be very similar to setting a transparent colour for a JPG - ie there are lots of areas which look green but on closer inspection they aren't - they are a slightly different shade, meaning there would be lots of non-transparent speckles everywhere.
TDK