can descendants of single couple multiply into large viable population ?

We had argument on IRC recently, whether, genetically
speaking, descendants of the single couple of humans can
grow into viable population ? (the arguments started from
somebody mentioning that [he read somewhere that] it
was genetically found that all native population of
one continent was descended from a single couple.)

Some people argued that it was impossible that inbreeding
and recessive pairing (correctme) makes the [whole]
population unviable.

Others argued this is possible, because even if some part
of population suffers from genetics defects, sufficient part
of population has healthily mixed genes

I think when animals migrate to remote places, like
to remote islands, there must be cases when single couple
produce viable population. I think this must happen with humans,
too, through the long history of human migrations.

But I'm not biologist and I can't really argue for this. So:
can descendant of single couple multiply into large viable
population ?

Yakov


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