Of course I'm sure that TimeMachine backs up the Photos library - As I said I use TM daily and I would not have suggested it otherwise - the Photos library is simply a special folder called a Package that contains many files - for a system stand point nothing different than a work document
and of course your new requirement that you use the EHD with other systems totally changes things of course, when you do not provide full details you do not get full answers
How do you want to access the photos and from what systems? Another Mac with the exact same OS and version of Photos? A PC? Another Mac with a different OS and version of Photos -- for anything except another Mac with identical software there is not solution I am aware of, it may exist but I doubt it
LN