The system will update regardless of the HC-300 not. I have done it as well as others. It won't even say update failed for the 300. It just doesn't update.
If you are getting failed to update driver are you sure the error pertains to the HC-300.
Also this isn't a 3rd party driver really. It's the generic controller driver with the search tag modified to ID a 300 via SDDP.
Use the Generic driver if you want but you then need to ID via IP.
I've had updates hang that had nothing to do with even having an HC-300 in the project. Sometimes it just didn't start director after and manually starting it lets everything else complete.
Now you can update without and ID later or do it before. In your case you may have other issues and want to add the HC-300 after.
Also be aware you likely aren't going to get support from C4, even if you use just the generic driver. If you need support you might have to remove in order to get your issue looked at.
Again this isn't 3rd Party, just something you can try, but should know that you are likely not supported in any way.