Transferring Catalina system drive to older Mac — possible?

Solution 1:

No.

2011 MacBook Pros and earlier are not supported by Catalina. The latest supported OS for those MBPs is 10.13 (High Sierra). While there might be hacks and system modifications to get Catalina to run, they will be unreliable.

Apple usually closes off new OSes to old Macs because they lack necessary hardware - in this case because their GPUs don't support the Metal graphics framework.

Generally, any given installation of MacOS should work on any Mac that the OS supports. I've cloned several Macs, but always in a 'forward' direction: G3 iBook 2003 to MacBook 2006 to MacBook 2009 to MacBook Pro 2012 to MacBook Pro 2014 (Tiger 10.4 to Mojave 10.14!!!)

Solution 2:

In the past, you could quite simply move a boot drive from one Mac to another & have it work as though nothing had changed. The only proviso was that both machines were of an age to know what each OS is, not too new, not too old.
I've been doing this with Macs for decades.

If the 'jump' between OSes would have required a firmware update, that may be a stumbling block, however, if the Mac you want to transfer the drive to cannot run the OS on the drive, then this simply will not work at all.