The Hyperpixel uses all of the Pi’s GPIO pins and repurposes almost all of them to alternate functions.
The fan shim uses the following pins
It “may” still somewhat work but just be on all the time with no control over on off. The LED and Button likely won’t work with the Hyperpixel installed.
You may also have clearance issues with the fan shim being blocked by the hyperpixel. You’d need a booster header and tall standoffs to raise the hyperpixel.
I don’t think there is a dedicated case for the Pi “and” hyperpixel. The Pibow Coupe case is designed for the fan shim though and the Hyperpixel should be mountable on top of it on standoffs.