I would say theoretical yes, but NO for 2 reasons:
1 . the amount of absorption of light from clothing far out weighs any reflection - clothing is just not shiny.
2. If a ray of light from the mirror does hit your eye and is reflected, the angle of incidence = angle of reflection so only a very tiny amout of light would be at an angle sufficient so that the ray would be reflected back to the mirror and then back to your pupil - ie the reflected image would be something in between the size of your pupil and your iris, and again very faint, if not, completely unnoticable. due to absortion again.