I am not an expert, but since Bible Analyzer allows the user to download a "portable installation" where the application itself and all the modules are contained in a single directory (example, using Bible Analyzer from a removable USB thumb drive), what you're asking should be possible.
Use Windows to map a network drive letter to the remote network file system, then set it to re-connect to the network each time you restart Windows. I have not tested it, but I think it should work.
What you are describing does work. I just tested it on Windows 11 and a SAMBA server (which could easily be configured as a "personal cloud" that I could access remotely). I do not have any other windows versions to try at this time but I imagine the supported versions on the download page (7, 8, 10, 11) would work which means it would only be accessible on one platform (two if you can do a portable installation with Mac, not sure if the Linux version supports a portable installation).
Unfortunately, I don't believe that is what gospatium is asking about (since they mentioned phones and tablets). If I understand correctly, gospatium is asking about a cloud-accessible app (internet accessible app) that works on at least five platforms (phones, tablets, and all three major PC platforms).
Anywho, I mainly just wanted to let you know that your suspicion about a portable network installation does work.