Do Thiel Audio CS3.7 Rock?

I imagine it could. The choice of pre might be very important. Both the Thiels and the Edge do stray from absolute neutrality in a similar manner, fortunately both hardly stray at all. With such a match, I would think that the choice of pre would be more important than usual. Avoid tripling up in the same direction. FWIW, and with no disrespect to Edge, but with Thiel, I'd reccomend Krell and Pass first, then Ayre before the Edge amps.

I tried my best to love the Thiel 3.7 and I have the uptmost respect for the designer. I found the speaker - when appropriately partnered - refined, neutral and to proffer excellent resolution. But, this speaker does not rock, not even when driven with 500 watts of power. I found the bass lean and incapable of digging the depths of other products from competitors such as Wilson and Nola.

Thanks unsound. Yep, had a Pass X350 many years ago. Brilliant vocals, pure as anything. But too much heat for my small room. Edge almost as pure, with more refined, solid, transparent bass. (I hear the later Pass amps have improved bass, but just as hot.)
Yep, you are preaching to the converted on the importance of a preamp (and the tubes that go with it, usually).
I use my Ray Samuels B52 headphone amp as a preamp with the Edge with some nice NOS Telefunken 12AU7s and like the combo very much sound wise. I'm now using Harbeth SHL5s but thinking of moving on.

The CS2.4 is an insane bargain with the proper amp and room. Sounds like you have great electronics. They will, can, and do ROCK.

Yes, Thiel loudspeakers do ROCK!  Happy Listening.