First, it's just plan unprofessional for Line 6 to just leave you hanging here for 6 months without even responding to your question. At one time, you question had a very simple answer. YES. In fact it says on the very top of the chart on your page where you see your add-ons :
"This following should appear in all your Authorized devices that support the add-on."
Whatever that means. I'm pretty sure that whoever wrote the sentence & never bothered to look at it again, meant to say, "The following should appear..." Which actually makes sense & means when you purchase add-ons they will show up in ALL of your devices that support those add-on types. POD Farm add-ons show up in all POD Farm type devices. HD add-ons show up in all HD type devices etc.
I'm in total agreement with your choice of tools too. I bought a GuitarPort in 2005 when everyone I jammed with would ask WHAT is THAT? But all I had to do was fire up my laptop, plug my Bose 301 speakers into my laptop, pug my GuitarPort into a USB port, plug my guitar in to the GuitarPort & start GearBox (the software before PODFarm that looked a lot like Amp Farrn does these days) & play a few notes & watch everyone's mouth hang open in awe. Not from my playing. Just because I go from playing a Roland Jazz Chorus 120 & jump to Marshall Half stack with every kind of FX gizmo imaginable in a flash. A few years later I bought a StudioPort UX2 or a POD Studio UX2 (they look exactly the same except that one is black & the other is red. I have one of each) & I felt like I had a whole recording studio that I could bring anywhere & carry the whole thing myself. There are a crazy number of toys in there. Amps & amps & more amps. Every size & kind of speaker cab, FX for days. Compressors & over drives & a million presets to get things rolling.
Just in case you ever come back & check this post or it sends you an email letting you know that somebody finally replied to your question after 43 years. I just couldn't take the fact that NO Body replied at all. Also, you may have found that your UX2 doesn't like Windows 10. I know mine doesn't or didn't. They both worked great in XP & Windows 7, but 10 has been a nightmare. I could go on & on, but I need to leave before they find out I'm gone & not in my cell at the institution.