Yes, coilovers will grip like crazy AND improve the ride significantly.
Slammed cars are dumb IME when they lose the ability to corner, go fast, etc. It's all fine to a point, but past that point it's just ridiculous, you've got this great chassis and car, but you can't take advantage of it.
Buddy converted his C5 Z06 to coilovers recently. In the races he was already doing well...but it's next-level now in how it grips in situations that blow the mind.
And yes, with an electronic suspension tune and lowering springs, you might get a not-bad-setup, I did this with my BMW, but still nowhere near coilovers. They'll ride much better AND do the other stuff (corner, lower it, etc.).