It is your option. It isn't required for any reason and there is no concrete evidence that removing blooms speeds up ripening. What it does do is trigger new green growth instead weather permitting.

So if you don't plan to cover or do anything to stretch out the season in any way and you don't want any green ones to ripen indoors then feel free to remove any blooms that develop after the date 6 weeks before your first frost date.

Dave

Today I removed ALL the suckers that have no flowers. Here in Long Island (NY) I hope we will have about 1 month of nice weather. 1 month might not be enough for all the late season tomatoes - that now are flowers - to ripe, but cherries and mid season will be ok.

According to a "tomato timeline" posted here before and linked many times, It take about 52 days from the bud to the ripe fruit. This is for large fruits in the middle of growing season. But it can take shorter/less time for cherry types/sizes and smaller tomatoes. But I think later in the season and in cooler climates it can even take longer.
So then you have to factor in the effect of late season cool weather that will slow down the growth and ripening of fruits significantly. For example my FFD is around mid November but our October weather will be too cold (and rainy/cloudy).

So I would count backward 50 days from my average frost date ( say Nov. 10 -20th ) and start my pinch off schedule ( Sep 20 to 30th). And that is an optimistic outlook here. Even then probably I will end up with plenty of green tomatoes to pickle.
So you have to decide what is best for you.