I guess my anecdotal evidence is as good as any. I know of
a polyamorous 'marriage' which includes a child (who post-dates
the relationship) which seems to work just fine for the people
involved. FWIW, it's one man, two women. However, it's not a
asymmetcal bigamous relationship in the sense of just a man
with two wives, if you catch my drift ;-)

One of the women is an old friend and colleague, and yes I do
'support' them in their committed relationship.