Is it permissible to add four continuous rak'ahs to the witr prayers with the intention of not making them witr, and would this addition be considered part of the Tarawih prayers?

There is no harm in adding an extra unit of prayer (rak'ah) after the Imam concludes the Witr prayer with the salutation. Then, the person can pray Witr at the end of the night, thereby attaining the virtue of following the Imam and the virtue of making Witr the last of his prayers. It is permissible to exceed two units of prayer in the night prayer, even if it is preferable to conclude with a salutation after every two units. This addition is generally considered part of the night prayer, and if intended as part of the Tarawih prayer, it becomes so.