IMO the blackmailing can't last more than two weeks max, the situation is different from marriage track, Imvaan were related to Chakor and second leads so they could show them cursing Chakor daily but villagers are just props they can't get too much ss. It's similar to when villagers blamed Suraj for Ragini's contract, we got a couple of scenes and then it stopped being relevant.
I can't see how Chakor being blackmailed will make the villagers like Karan, whatever she'll do will be to benefit his plans and he won't pacify the villagers because if he was ready to compromise he would've let the bridge stand.
Any mu with the villagers will be that they think that Chakor supported Karan over them, for example not supporting the villagers if they seek compensation due to the accident.
I think if Chakor accepts Karan's conditions it'll only lead to Karan gaining control of Azaadganj and ruling it. Afterwards stealing the idol will be easy just like it was for Imli. I just hope that Saanvi is safe with Chakor.