Yes but I would recommend you the Live Link recording , it is easier and looks better.
If you don't have Live Link or CC4 only you can use this way but you will need the MH Live Link Kit , it is free ... Here is what to do for CC facial import to MH via FBX :

Is there a way to export FBX facial animations to Unreal Engine for Metahumans?

OMG! Thank you so much. I seriously need to learn more about the retargeting system. I can't believe it was that simple. Thanks!!

Don't know what went wrong in your project , could be the MH Version ( older or upgraded ) but it is easy to fix :

I did the same process on this video. And the shoulders and arms keep getting wonky.

  

Thanks Style Marshal! I'm a big fan! I have tried everything.  Here are links to the project files and an FBX https://drive.google.com/drive/folders/16Jko3vxPmwgUuroKtqUU4JDBWhrauVK4?usp=sharing
And here is the Unreal Project  https://www.dropbox.com/sh/74zaq1fjdp53oty/AAAVW5W1WB3sDBtkh670cB6_a?dl=0

I seriously think something is goofy because I used Motion Director to animate the walking. Then added the arm animation. Then flattened it. On the project named "Mocap_Fix" I zeroed out the animation to start at the World Origin point, but it just keeps messing up.

 I'm going to try using the motion file on a different body type. I'm also going to try starting a new project file and applying to the same body type again. I may have to uninstall and reinstall iClone 8. I already uninstalled and reinstalled UE5.2.1 yesterday. 

I guess you forgot to deactivate Live Link for the MH body after recording , it is working fine here (UE5.2.1) , see video ( showing FBX import and Live Link recording ) :
Also be sure you are using the latest versions of CC_Setup , IC Live Link and Live Link MH Kit from Reallusion.

I spoke too soon. Looks fine in Live Link when recording but when I play it back, it gets even worse. And its still stationary. I have no idea what's going on. SMH

The imported FBX on my laptop went back to being hyperextended and wonky for some reason. Earlier it was fine. Well the character looks fine using Unreal Live Link. The export to FBX option is broken now though.  Thanks again. 

So it worked on my work laptop. But when I got back home the same method didn't work. Sigh. I'm deleting the Metahuman and redownloading fresh like I did at work now. Hopefully this works. If not, I can only think to delete and reinstall UE5.2.