[Yodaman]

Looks like it should work fine. Personally, I run firring strips vertically down the roof so water channels straight down without obstruction. And the plastic coming down over the sides has created a parachute for high winds.

 

[Yodaman]

So is it time to re-roof or re-tarp? If the later, I'd skip the poly and use medium duty or heavy duty tarps. Hold it down with furring strips running longitudinally down the roof. Use a few cap nails on the lower edges, so water could run out if needed.