You are going to run into registration issues running from the USB stick; this won’t matter for the beta, which is just going to expire at a set date and that’s that, but for the regular version, some registration information will need to get written to your computer’s registry. Additionally, there are files that are created in your user AppData folder which will either be created when you save them on a given computer (compile presets, project templates, backups, etc.) or, conversely, will not be accessible if they were created on a different computer. The spellcheck dictionaries will probably also not work for most of your machines if you are not installed locally.
Basically, Scrivener isn’t currently built with the intention of being able to run off a USB drive. I know some users do it, but it’s not a set up that we recommend or support, so just be aware that you may run into some quirks if you’re trying it.