Well, I found something in an article about the E-2D that seems pretty significant.
"Why is this a major advance? It turns out that continuous scanning across the full 360 degrees limits power applied in any one direction. To keep the scan revisit rate relevant, the radar can only spend a brief instant on each degree of arc before sweeping around again. That is usually more than enough to pick up a target and establish its track. But what if the target is especially hard to see – i.e., stealthy? Or what if it is flying low in ground clutter? In that case, what’s needed is a focused beam that dwells longer, sending more energy in a specific direction. Increased energy transmitted out produces more energy received back and a sharper radar return.
The E-2D for the first time combines both modes in a naval platform. Electronic scanning enables the radar to function both as a rotating beam generating 360-degree coverage, and as a staring beam that can pour radar energy into tracking even the smallest, stealthiest targets. As a result, the E-2D radar is so flexible that its crew can rapidly switch between three main modes of operation. First is the classic rotating beam, ensuring the strike group has no blind spot. Second is a mode which continues the rotation but carves out a 45-degree slice, for example, where power is enhanced. The crew can focus the beam at the direction of a known or cued threat and boost the power while the beam is pointing that direction. It’s the equivalent of scanning the horizon but pausing briefly to stare especially hard at the area of interest. Finally, the E-2D can temporarily turn off the rotating function and funnel all its considerable radar energy at a target."
It seems as if the E-2D will have the ability to focus its entire energy on one single target, allowing it to establish a more solid radar track. It seems to me (although I could certainly be wrong) that this would allow the E-2D to detect the low-observable target in normal operation, then focus on it to actually be able to get a stronger return, track the target, and use CEC to engage the target with, say, an SM-6. Obviously, I don't claim to be an expert (which is why I'm asking you guys), but that seems plausible to me.
Also, I would definitely agree with all the people who have posted that no radar system is perfect or capable of everything -- I certainly don't want to seem like I'm making that claim, or being a E-2D fanboy.
Finally, thanks for all the answers! I'm glad to get the feedback.