Catalina on USB

Similar to Mojave, if you can get it to install and boot, sure, there is no reason you can't -run- Catalina from an external USB-C drive. Given the hiccups involved w/Mojave, however, I'd not bother. If you need to include an external, try parking your Home folder on it, instead, and use FUS to get in.

I did this, because I expected I could avoid issues with my main boot drive. But something went pretty wrong with the Fusion drive when it mounted under Catalina, even though I hadn't booted from it. I suspect it has to do with the way that I created my BootCamp partition for this 2012 iMac, but who knows? All I know is that my boot disk ended up in a semi-unusable state, and I spent the next couple days working my way back from the backup I had made the day before.

Moral of the story is to not assume that your boot disk will be unaffected, even if you have installed to an external.

Yes you can. On T2 equipped machines you have to enable external boot in the Startup Utility on th Recovery partition.

Found it.. needed to partition as APFS. Now installed/running off a bootable USB Drive.