"Green roof" can't be uncountable as it is a roof! I would expect to see "A green roof..." (as in Wikipedia).
I would also add that roofs don't grow plants, gardeners do. So I would prefer "that has plants growing on it." A roof is already on the top of a building.
It is possible that if the roof has been trademarked (i.e. Green roof®), you might write it without an indefinite article.
They might say that if they've never heard the phrase.
If you say to them that you are going to get a green roof, they are more likely to say "What's a green roof?", although they could say (probably less likely) say "What do you mean by green roof?"