Sunil,
It is possible to burst reports to BI Inboxes. I had figured this out a while ago, but forgot to post the solution here.
You will need to create 2 things.
1- A set of user groups that contain the users identified for BI Inbox distribution.
2- A User Profile that will contain the mapping information between the above user groups and the filter criteria associated with each group.
Once these things are defined, you can create a publication that distributes off Enterprise Recipients (List all user groups you create in 1) and contains the profile mapping(the profile you define in 2) against the filter condition of the report under Personalization section.
Hope this helps.