On left, after 3 weeks. On right, just picked.
Yes, green tomatoes will ripen. It takes 3-4 weeks.
This year I had only a few pitiful tomato plants. Two here and one at the lake. They barely produced, so each tomato was precious.
The red tomato on the left was picked three weeks ago when we closed the cottage. The green tomato was picked a few days ago when we finally had a hard frost here.
Low humidity, northern light, and time did the trick.
Other ways to ripen tomatoes:
Place in a bag or box with a green-ish banana--or an apple---to release ethylene gas to help to ripen them. Check daily.
Or wrap individually in newspaper, no more than 2 layers deep, and place in a dark, dry area for 3-4 weeks, checking periodically for any sign of rot, so you don't lose the crop.
There may be other methods, but that's what I have learned.