It would depend on how much the cover is, how long it's for and what they actually cover.
The only issue that I had with my roof is in the seam line, they would probably argue that this wouldn't be covered as the roof stretches when it is put up/down. I have solved this thanks to Wills370 as he recommended stormsure a waterproof glue that you use on boats and touch wood it's worked a treat.
I personally don't take out extended cover on anything as it's normally not worth the paper it's printed on. Imho.