No you can't add single books to a user category.
The closest you can get is to use the "Reading list" plugin, this gives you the ability to add single books to a list. However it won't achieve your second objective of being able to list them in the tag browser - you can only view the list in your main library view or in a popup modal dialog.
As an aside - perhaps one day the Tag browser could be expanded to allow something like the Reading List plugin to put its own lists in there as another extensibility point... if chaley spots this he may care to comment. I can appreciate it is likely a lot of work from his side and might be a non-starter but if you don't ask you don't get...