Restore Time Machine Backup of 2016 MBP to 2011 MBP?
You could install the macOS you want on the old machine first to be sure it runs. Get all the work done before you upgrade the component. Even if the specs are OK, I like to know everything is in working order. The OS only needs 15 GB or so to install.
As long as you can run the same or newer OS than was backed up, you’ll be able to restore apps and data.