One must do Agnyaa Kainkaryam though there is no relationship between this and attaining Moksham because performing Sarangati will lead to Moksham. Not performing Agnyaa kainkaryam will beget sin and we have to undergo punishments for it; so, it is a must that we do Agnyaa kainkaryam.
Karmayogam stated in Bhagavad Gita and Agnyaa kainkaryam are not the same. Irrespective of Karmayogam, Bhaktiyogam, or Gnanayogam, Agnyaa kainkaryam should be done separately. Nitya karma anushtanam-s can be considered as Agnyaa kainkaryam which should be done every single day without fail.