i had started an air layer for a papaya a few months ago.
i removed the plastic after 1 month and there were 2-3 small root hairs.
i got busy and forgot to re-wrap it... LOL
its obviously possible.
ive grown a couple from cuttings as well,
but, the ones i tried from the leaf-stems didnt work, only the ones from growing tips worked.
they do grow very fast from seed, but for me, this may actually work better
in years with mild winters, most of my papaya make it through
in years with cold winters, i loose most of them,
or, they freeze to the trunk, and take 2 months in spring to produce a flower.
and another several months to ripen fruit.
this way, i can have smaller/shorter plants in the greenhouse over winter
and i can do a cutting or air-layer in early spring of a fruiting pant
and it should produce for me much faster.
cutting grown