Think of who else does street work like this, and the signals it may give to your target audience. I would worry that such an approach would be mistaken for Scientology street recruiting (compare it to "Discover your true potential" and other such come-ons for their introductory "personality test"), or similar street work by some other religious group, and might be avoided by exactly those people you might wish to reach.

In the evangelical days of my youth, this sort of thing is exactly what we were encouraged to do: get strangers talking about a "deep" subject that provided a natural transition to just how bleak things are without god, the fulfillment of salvation, and so on and so forth.