If there is any corruption while writing the data to PRIMARY File Group's files the database will not available to access. We can make the Database available by adding Secondary FG and placing the data to this Group.
No, absolutely not. If there's corruption in the primary filegroup then you need to restore or repair the database, restore preferred in most cases.
I think i have asked the question wrongly, here
1. With only Primary File Group.
The user data will be written to the Primary File Group, if there is an error while writing, Is this database will be available?
2. With Primary and a Secondary.
If we write all the user data to secondary File Group, and if there is any error while writing the data, Is this database will be available?