That's an interesting question. Since all that matters is the light that the chicken's body (probably its eyes or head, but I am not sure) is exposed to, then as long as they would USE the run whilst it is artificially lit, then I can see no reason why that wouldn't "count".
However, since in a small coop like that you can use a really small bulb (possibly even a nightlight; or a short LED xmas-lights string) that can tuck neatly out of the way in a corner or such, it seems very very unlikely to me you couldn't fit it into the COOP if you prefered.
Note that it is likely getting a bit too late in the year for adding light to have much effect. I'm not saying don't try it, I'm saying don't hold your breath
-- we're only, what, six-ish weeks now from the shortest day of the year, and days are really pretty short up here. For best results you really ought to add light as soon as natural day length (as experienced by chickens, which can be shorter than dawn-to-dusk if your coop is in a dim location) drops below 14 hours a day, which in Maine may be as early as late August or certainly sometime in September.
As far as plastic-covering the run, I do that too, and have had better luck with 6 mil (the stuff sold as vapor barrier for houses) because it holds up better to rustling in the wind; but certainly you can TRY the 3mil if you've already got it on, just you may need to replace it before winter is over. I find that it holds best in cold windy weather if you tack it on in just a few places with a staplegun, then tape duct tape along where all yer staples are going to be, then staple it on thoroughly THROUGH the duct tape. Make sure to leave a generous sized area -- I would suggest at least 1/2 of one side -- open to prevent humidity buildup.
Good luck, have fun,
Pat
