1. *It would have been a good idea for him to have gone to that school*.

Does sentence (1) *alone* provide sufficient information for the reader/listener to assume that "he" didn't in fact go to that school? Or do I need to follow it up with another negative/positive sentence to make the intended meaning clear, as in:

2. *It would have been a good idea for him to have gone to that school. But he didn't go there*. Or
3. *It would have been a good idea for him to have gone to that school. But he went to another school*.

In other words, could I use (1) if I don't know whether he really went to that school?