I have never raised chuckars but I have hunted them a fair amount in several western states. Their prefered habitat is very hilly steep inclines, I always remember big rocks also. The typically run not fly from danger, the rocks must give them dodge exits I guess.
I would think unless your habitat close by is not suitable they would either be goners or would find habitat to their liking.
And when I mean steep I am talking a 30-40 degree incline, I have never seen one on anything close to level ground.
Don't know how many you have but you might try letting a few out of the pens and keeping the rest locked up. That would be strong incentive for the free ones to stick around, if they disappear, you have your answer.