If an INNER JOIN in a query returns no rows, do additional INNER JOINS add a significant performance overhead?
The order in which tables are joined isn't defined in the query (unless you use a join hint, which I wouldn't recommend), so you can't be sure that A is joined to B before B is joined to C.

To answer your question, in most cases SQL Server can tell from the statistics on the table (or other criteria) that the query won't return any rows. In that case, another JOIN won't make any difference from a pure performance perspective.