I don't see why not, but a 'cleaner looking' solution may be 2" grey PVC. (ending in a 4" to 2" reducer 'T') Just a thought. Shouldn't be a need to glue it together, as it slides together pretty tight.
But, as long as you do something that works, then go for it. :thumbsup:

If doors aren't weather-stripped, air will come thru there, inherently adding to the intake volume. (it'll leak air in, which is ok as long as the light doesn't follow, lol)