They can certainly survive without the men. There are a few island events that introduce new villagers in VV2, so the best you can hope for is to have one of those. With my luck, I'd probably get another girl!
That's what happen on my VV1 game; one man waiting for the ten year old girl to grow up. They had five children before he died; all girls. Then, after the mum died, the girls found a crate with an todder inside. You guess it; another girl.