Main characteristic of short circuit evaluation is that it stops evaluating the expression as soon as the result can be determined. That means that rest of expression can be ignored because result will be same regardless it is evaluated or not.
Binary boolean operators are comutative, meaning:
a AND b == b AND a
a OR b == b OR a
a XOR b == b XOR a
so there is no guarantee on order of evaluation. Order of evaluation will be determined by query optimizer.
In languages with objects there can be situations where you can write boolean expressions that can be evaluated only with short circuit evaluation. Your sample code construction is often used in such languages (C#, Delphi, VB). For example:
if(someString == null | someString.Length == 0 )
printf("no text in someString");
This C# example will cause exception if someString == null
because it will be fully evaluated. In short circuit evaluation, it will work every time.
SQL operates only on scalar variables (no objects) that cannot be uninitialized, so there is no way to write boolean expression that cannot be evaluated. If you have some NULL value, any comparison will return false.
That means that in SQL you cannot write expression that is differently evaluated depending on using short circuit or full evaluation.
If SQL implementation uses short circuit evaluation, it can only hopefully speed up query execution.