Even turf is heavy. I would say 'No'.

I'm just wondering what a 'patio roof' is - do you mean some kind of porch extending out over your patio? Even if its supported by brickwork, its unlikely to be weight bearing, and that you need to establish before using it as planting space. Plants in pots are pretty heavy, and even proper extension roofs can be either weight bearing or non weight bearing. For weight bearing, the construction is somewhat different.

Not a good idea, I'm afraid. Green roofs need to be properly constructed to bear the weight of the growing medium.

It's even heavier when wet and in wind it can be very dangerous. Besides if you are sitting on the patio, how are you going to see the plants over your head? I think that this is an idea that should remain just an idea.

If the roof is supported by pillars you might grow clematis in large pots to climb up the instead?