Up north I lived in a triple decker with landlady on the first floor. Her very small backyard was paved with asphalt. I guess she was not a fan of grass, though she grew collard greens by the side of the house in dirt that must have had lead in it. Portuguese love their collards and linguiça soup.
In the middle of the asphalt she had punched trough it, and grew a concord grape vine that really thrived. The stem was 3-4 inches diameter. It climbed up to a 12ft x 12ft trellis that gave shade in the summer. So your passion fruit project should work out. Passion fruit vines are powerful growers that can climb up to cover entire trees. I have seen the photos from the Caribbean islands.