Yes and no.
(Below refers to SQL Server exclusively)
Some operators short circuit and some don't.  OR CAN short circuit, but may not depending on the order of operations selected by the query engine.
CASE is (I believe) 100% guaranteed to short-circuit.
You can also try to force order of evaluation with nested parentheses, like:
IF ((X) OR Y)
But I'm not positive this is always consistent either.
The trouble with SQL in this regard is it's declarative, and the actual logic is performed by the engine.  It may in fact be more efficient to check for Y first from your example and then check for X - if, for instance, Y is indexed and X requires a table scan.
For Reference:
From the ANSI-SQL documentation from this answer:
Where the precedence is not determined by the Formats or by
  parentheses, effective evaluation of expressions is generally
  performed from left to right. However, it is implementation-dependent
  whether expressions are actually evaluated left to right, particularly
  when operands or operators might cause conditions to be raised or if
  the results of the expressions can be determined without completely
  evaluating all parts of the expression.