Based on my experience, ATC Radar have no difficulty seeing commercial aircraft with a high probability of detection and low probability of false alarm.
Source: completed a performance assessment of several such systems in the early 2000s against their legacy counterparts using aircraft beacon systems as a source of “truth”.
If I remember to come back to this later, I’ll write a little post showing the theoretical detection performance of such a system. If you’d like to try the exercise yourself, the relevant worksheet is a Blake Chart and you can look up surrogate parameters for the Radar via checking the ASR-XX pages on Wikipedia (e.g. ASR-9 or ASR-11). Finding Radar cross sections (RCS) for commercial aircraft models is similarly straightforward. The system is logarithmic so as long as you’re in the ballpark you’ll be close.
The JSS is a descendant of the SAGE system developed during the Cold War to detect soviet aircraft. It has a reduced equipment footprint, but this is generally due to improving radar technology, coverage is similar and the backend data processing systems are much more advanced. The majority of radar sites belong to and are maintained by FAA but report directly to the Air Force air combat system.
I'm not sure exactly what equipment is installed there, I found an older report listing an ASR-8 at that location but that system is obsolete and inconsistent with a newer list showing it as a secondary (SECRA) site only.
Consider that controllers currently rely primarily on secondary radar, which while more difficult to spoof than ADS-B is still quite subject to malicious manipulation. They are well aware that a primary radar return with no corresponding secondary radar information is something to sort out, and this won't change with a switch to ADS-B.