It's not a rule of English grammar that you can add -ee to any verb to describe the subject.
It should be seen more as a common approach to creating a new word. Like any new word, or neologism, the resulting word still needs to be accepted by the community: many new words fail and die because people just don't like them.
You will find that in some cases, people can guess the meaning of your new -ee word, and accept it. In other cases, they might be confused or just dislike it. Many people might be resistant to the whole idea of inventing new -ee words and find the word "distasteful" for that reason.
The -ee words you could think of, like "employee", are neologisms that have gone through the "acceptance process".
Either way, it's a new word that you've created, rather than a product of standard grammar, and you should bear that in mind. If you were writing something formal, you would not normally include any neologisms - they are more well suited to something more light-hearted.
EDIT: the following page lists the -ee suffix words which have entered the language to date. More may enter in the future.