Depends on whether the person is aware his choices have enslaved him or not and whether he still has the free will to choose otherwise again. If they are fully aware and still have choice to remove themselves from the shackles then no they are not a slave, but if once chosen the path there is no way out most definitely they are a slave.
If they are not aware of it no matter the circumstances they would be a slave but not knowing is almost a blessing as the oppression would not be directly noticeable and just seem as part of normal life. I would call them slaves of the mind more then anything.
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