Resolution:
Yes, it is possible to trigger publication based on Child Business Component.
E.g.: A publisher is configured with 'Account' as top level Business Component and 'Contact' as its Child Business Component with event script written on BusComp_WriteRecord () of 'Account' Business Component to set required values of input property set. The issue here is whenever Account is modified through Siebel client and the user tries to enter Contact details by going to that tab in below applet, the event is fired and adapter publishes only the parent BC data without Contact.

The problem with writing the event script on parent (Account) business component is that the script gets executed immediately after the parent record gets committed to Siebel. As the child Business Component is not yet inserted, adapter will not be able to publish the child (Contact) information.
To publish both Account and Contact, you could write an event script on child Business Component and in the script, fetch the value for the field (the field that you want to use as 'Key Field' for the parent) of the parent and pass it as the 'Key Value' to the Business Service.

Can publishing be triggered based on changes to the Child Business Component?