If an INNER JOIN in a query returns no rows, do additional INNER JOINS add a significant performance overhead? If I make a query as follows:

SELECT *
FROM TableA A INNER JOIN TableB B ON A.AID = B.AID
  INNER JOIN TableC C ON B.BID = C.BID


Does the INNER JOIN with TableC add significantly to the performance of the query? Will it attempt to do the join, or will it note the empty set of records and move on?
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.