Using the transversal vibration resonance of a suspended carbon nanotube as a charge detector for its embedded quantum dot, we investigate the case of strong Kondo correlations between a quantum dot and its leads. We demonstrate that even when large Kondo conductance is carried at odd electron number, the charging behavior remains similar between odd and even quantum dot occupations. While the Kondo conductance is caused by higher order processes, a sequential tunneling only model can describe the time-averaged charge. The gate potentials of the maximum current and fastest charge increase display a characteristic relative shift, which is suppressed at increased temperature. These observations agree very well with models for Kondo-correlated quantum dots.