No, only the file contents are encrypted. The file names and folder structure is visible to anyone who has access to the files.
The files themselves can contain a ton of stuff if you want, but the convention is to put the password on the first line and that's what "pass -c my/file" will copy.
pass probably isn't for you then, unless you find a wrapper or something that lets you put all in one file. I've switched to keepassxc as well, I could never get the browser integration to work with pass.