Yes, to a degree.
I wonder how, because I can just click 'allow' and 'continue' and get access to all my stuff.
As can I, but if you give me a second I'll find a folder where I can't click allow/continue.
edit: found it.
I cannot access that folder. Not that I generally want to, but I can't access some other folders on there either, such as \cookies and \documents
How did you get that folder? The built-in Administrator account is disabled by default. Note that if you enable it, UAC doesn't apply to that account. So if you want to temporarily work without UAC, logging in as the built-in Administrator is a good way to do it.
Under default settings, only the user that created them can access their personal folders. Administrators can too, but with UAC, that only applies if you're elevated (except for the built-in Administrator account, see above).
And as Paolo explained, Application Data is a junction point, you can't access it. You want AppData instead.