This CodeProject article All About TransactionScope
] goes into some detail about the TransactionScope class, which may help you.
You also need to be aware of an issue with the class for use with SQL Server - see this article using new TransactionScope() Considered Harmful | David Browne's Web Log
My gut feel would be that the new lines of code would not
inherit the isolation level, in the same way that if isolation level is set within a stored procedure in sql, the isolation level reverts back to whatever it was when the SP terminates. You can prove or disprove this by creating a new transaction (without setting isolation level) and querying the Transaction.IsolationLevel property.
If this is being used for a SQL Server connection then you can confirm or deny the behaviour by querying the Isolation Level currently on the connection (assuming you are using the same one) - This article has some C# code for doing that Getting and setting the Transaction Isolation Level on a SQL Entity Connection
Try for the empirical evidence in whatever you are using TransactionScope for in your own code.
Personally I would never assume that the level is inherited and would explicitly set it myself.