Yes you can take them out and let them
finish carbonating.
Next time don't touch them for 3 weeks.
The
3 weeks at 70 degrees, that we recommend is the
minimum time it takes for average gravity beers to carbonate and condition. Higher grav beers take longer.
Stouts and porters have taken me between 6 and 8 weeks to carb up..
I have a 1.090 Belgian strong that took three months to carb up.
If you just arbitrarily put them in the cold at three weeks,
without making sure they were carbed to begin with, then you've prevented them from carbing further.
Yeast go to sleep in the cold, they don't carb your beer. SO of coulrse you beer is stuck uncarbed right where you put them into the fridge.
Temp and gravity are the two factors that contribute to the time it takes to carb beer. But if a beer's not ready yet, or seems low carbed, and you added the right amount of sugar to it, then it's not stalled,
it's just not time yet.
Everything you need to know about carbing and conditioning, can be found here
Of Patience and Bottle Conditioning. With emphasis on the word,
"patience."
Don't put them into the cold until you know for sure they are carbed. You can't carb in the fridge. The yeast will go dormant in the fridge and not produce and co2- you'll have flat beer no matter how long you leave them in there.