The problem with Afterburner 4.4.0 final and the Crimson Relive 17.1x.x compute drivers seems to be related to using the pixel patcher.
https://forums.guru3d.com/threads/afterburner-fails-to-display-clocks-on-patched-crimson-17-10-drivers.417926/
Unfortunately with RX 470/480 and 570 cards you must uses the pixel patcher to bypass the driver signature check when using a modded Bios. With most RX 580's you don't need the pixel patcher. I reverted back to using the blockchain drivers on Windows 10 v1703 and Afterburner is working.
https://support.amd.com/en-us/kb-articles/Pages/Radeon-Software-Crimson-ReLive-Edition-Beta-for-[Suspicious link removed]pute-Release-Notes.aspx
https://forums.guru3d.com/threads/afterburner-fails-to-display-clocks-on-patched-crimson-17-10-drivers.417926/
Unfortunately with RX 470/480 and 570 cards you must uses the pixel patcher to bypass the driver signature check when using a modded Bios. With most RX 580's you don't need the pixel patcher. I reverted back to using the blockchain drivers on Windows 10 v1703 and Afterburner is working.
https://support.amd.com/en-us/kb-articles/Pages/Radeon-Software-Crimson-ReLive-Edition-Beta-for-[Suspicious link removed]pute-Release-Notes.aspx
Just signed up to thank you for this post. I figured out that I had to roll back my driver to the Crimson Relive 17.8.2 http://support.amd.com/en-us/kb-articles/Pages/Radeon-Software-Crimson-ReLive-Edition-17.8.2-Release-Notes.aspx (the one you linked to is bugged for me and others according to the patch notes) to keep the Afterburner compatibility.
Although I will say that I had this issue with the RX 580s, so I don't think it has to do with the pixel patcher since, as you said, you don't need to use it to mod your bios. Seems like it's an issue with Afterburner but obviously I can't know for sure.
