Suppose the intruder was not transmitting Mode C, thereby rendering TCAS (if fitted) inactive.
It doesn’t. The TCAS would still show a return, but without a relative altitude.
However, that still causes an issue. Knowing that there is another aircraft laterally close by and potentially conflicting, but unable to know whether to look up, down, or wherever, is very bad for the blood pressure. I was in that very position less than 24 hours ago.
Mode C is a legal requirement for IFR flight but there is no way of knowing if a “Mode A only” aircraft is actually flying clear of cloud or not at that particular time because a pilot could ignore that requirement, or have a failed Mode C and be blissfully unaware, especially if not talking to an ATC unit.
Discorde, I see you have edited and corrected your post since I began my reply. 😎