You would have to be REAL REAL POSITIVE that the coop will be 100% shaded (not dappled shade) for ALL the daylight hours during ALL the summer i.e. late April through late September. (I grew up just outside Philly, I know the climate
)
The difficulty you will run into in the wintertime, though, is that when outdoor temperatures drop below freezing, or if there is for any reason a large difference between in-the-coop and outdoor temperatures in the wintertime, you will get a lot of condensation/frost forming on the underside of any uninsulated roof, which will increase humidity in a way that normal ventilation can't do away with.
So with an uninsulated corrugated-plastic roof, you will have humidity problems for a significant part of the winter. The solution is of course to INSULATE the roof, but then it isn't clear anymore
-- if there is only a minor condensation problem (temps are not too cold, and not too different indoors vs out), and not very many chickens per size of coop, and coop is very well ventilated in winter) then taping a layer or two of bubblewrap up there may give you sufficient margin for error -- but I would totally not count on it. Particularly since your whole POINT in using the clear roofing is to try to heat up the coop in the wintertime. This will make the coop air hold more moisture during the daytime (warm air inherently holds a lot more water vapor than cold air -- its absolute humidity is higher at a given *relative* humidity that's the same betw cold and warm air), which will then condense out the inside of your roofing panels at night and cause problems.
So, I mean, you can do it, but you won't get all that much benefit out of it, so I am not sure it is worth the (modest) extra expense and the aggravation of fiddling with insulation arrangements. Corrugated metal panels are usually a bit cheaper than polycarbonate (and you would probably not want to use the cheaper pvc, as it is quite vulnerable to hail damage); you will have to insulate them same as the plastic panels, of course.
Good luck, have fun,
Pat