When I grow gourds I leave them on the vine all the way until frost. Ideally, they ripen and dry on the vine before the frost hits, but the further north you go, the harder that is to achieve. But if the gourd is still green but has gotten to its full size, you'll usually still be successful. With green gourds, I always leave them outside and if you can hang them up high, like in a tree, that'll be better because they get better airflow which helps dry them quicker.
My experience in curing green gourds is pretty good. Maybe 25% rot and mush but 75% cure properly through the winter.
You could probably cure them indoors but you'd need a lot of airflow.