That all depends on If the parents have the O.C.I already in their hands or not.
Even if the parents did NOT have the O.C.I in their hands, and parents want to apply as a family, in other words they want to apply for their children as well as parents at the same time, then they may do so without any trouble.
There is no law that state that children have to be here in the states.
But, if the children are in India, and they are able to sign ( signature ) their O.C.I applications, then how do parents coordinate the signature part of the applications, that is something parents need to think about before applying for the O.C.I.
also, the passport size pictures that are supposed to be affixed on the O.C.I applications, how do parents coordinate this with their children? I guess children could go to the nearest photo shooting place and get their passport size photos and mail them back to states, and they can also manage the whole thing with the signatures like that too, where children might be able to sign their respective O.C.I application and send them back to states as well.
I guess the best advise is to hire an immigration lawyer resides in States and knows Indian Laws inside out, and also knows the Immigration laws here in the states, and has the license to practice in the region you reside in.
good luck.
Please post back as to what you decided to do, and what were their results.