First of all "Will Purvi be able to take Archana's place " - Will a daughter be able to take a mother's place ?
Nope.
A mother is a mother and daughter is a daughter.A daughter can become a mother but no one can replace a mother. Children can be a support but can never replace a mother.
So the entire question does not make much sense.
Archana as a character cannot die in the show as the show is all about Archana and Manav.so its out of question.
Ankita leaving the show does not mean the character Archana might die.They might introduce new actor.So here no character is replacing any character. The only possibility is actor getting replaced which is still under speculation.
Ankita has lived through Archana's character for three long years n she is a household name both in India and internationally as well.
She has a very huge fan base like Sush and Zee has recognized her as Zee brand ambassador and she is very important to Ekta n PR team.
Anki quitting the show or not is Anki's choice n we fans are with her no matter her decision but Anki's quitting the show wont kill Archana the character.But majority of viewers wont be able to accept anyone in place of Anki as Archana (this is a different story all together n Zee/Ekta know about it n the dangerous effect it will have on the show so called TRP).
I am sure Ekta/Zee will come up with some thing that either drops the pregnancy track or something to convince Anki from leaving the show.Only time will answer on that.