In reality, pretty grim. Mrs. Howell would seem to be beyond her childbearing years, leaving Ginger and Maryann. Gilligan and the Professor, being the two youngest, seem like the most probable fathers for the first round. The girls are likely to leave the fossil-hunting (searching for an old bone) until later.
It is true that women having been having babies since before historical records. It is also that before modern obstetrics infant mortality rates were high.
Also, once born people don't live forever. Three of the castaways were already in geezer mode, and there are accidents and diseases that could take out more.
My guess is that their numbers would somewhere between 6-15, at best. And life would be even less grand for them without access to education, medicine, and technology. This last one is mostly important to belief. If you had never seen phones, lights or motorcars, how likely would you be to dream up an iphone, an Alexa, and a self driving electric car?