Yes, your revised query would return the result test rows that had a value of "something" in t1.col1 where there was no row in t2 which made the ON condition t1.idcol = t2.idcol. It is important to note that if t1.idcol is NULL, it doesn't matter if there are any rows with NULL in t2.colid or not for two different reasons...
Most importantly, NULL is by definition not comparable so it is never "equal to" anything, not even another NULL (which is why you must use the "IS NULL" predicate instead of using = NULL in its place). Even if that weren't the case, the value would still be NULL if the join succeeded, so the code wouldn't be able to tell any difference!
-PatP