You can pick them much earlier, and they’ll continue to ripen off the vine.
I sometimes do that with the tomatoes I use for cooking. However, some varieties, like Ananas Noire, only develop their full flavor on the plant. When they ripen after picking, they become sweet but lose some of their rich flavor compared to when they ripen on the vine.
Generally speaking, if you pick tomatoes when they’re half-ripe, the flavor will still be good.
Yeah, a bunch of people suggested that on another thread, so I tried picking mine when they were fully grown but still green. Unfortunately, they didn’t ripen properly and just turned yellow and gross. 
I don’t pick them when they’re green; I wait until they’re orange or slightly red.
You need to wait for the blush. Tomatoes won’t ripen off the vine if they’re picked while still fully green.
It’s not necessarily true in all cases.
This year, the only way I’ve managed to get tomatoes before the critters is by picking them green or just barely blushing and putting them in a paper bag to ripen on my kitchen counter.
I always pick all the green tomatoes the day before frost hits and store them in small cardboard boxes or paper bags (don’t stack them; only a single layer at the bottom of the bag or box). They slowly ripen and provide me with tomatoes for nearly the entire winter. 
Yep! Our weather has been terrible this year, and my Roma tomatoes just wouldn’t ripen on the vine. I pulled them all off and have been ripening them in cardboard boxes with bananas. It’s turned into a beautiful science project! 
I had a storm knock a bunch of green cherry tomatoes off the vine. A few weeks later, I noticed one I had left in the pot had turned red. It confused the heck out of me because I’d never seen it happen before. (And yes, I’m sure it wasn’t a different one that fell. I pick them when they’re blushing, and it’s a small plant where tomatoes can’t hide.)
I picked almost all of my tomatoes fully green this year. I put them in a brown paper bag and let them sit for 7-10 days to ripen.