It should do. I think it depends a bit on the room temperature, your case and it's cooling. It is better to have some headroom. Strange that the "regular" Dark Rock doesn't fit. My 2nd PC is a 5600X on a X570 Asus board, 4x 3600Mhz memory sticks and a Scythe Mugen 5 (with 1 fan), without a problem. Think it is about about the same size of the Dark Rock. The Scythe Mugen 5 keeps my CPU idle at 31 degrees celcius and under Prime95 at 60 degrees, running up to 4.7ghz. But I must say that I have a good airflow in my case. Do you use 3200Mhz memory? If higher, there is a good chance your CPU will overclock.
7700X - X670E-F Gaming WiFi - XFX RX7900XTX Black Edition - 32GB Trident Z5 NEO C30 6000MHz - 1x1TB Samsung 990Pro, 2x2TB Samsung 980Pro, 2x 2TB SSD - MasterCase H500M - Super Flower Leadex Platinum 1000W.