Sure, but playing the tones of the dorian mode is not enough to make what your playing sound "dorian". What enables your playing sound dorian results form a prioritization of certain tones, by giving them more emphasis via rhythm, accent, duration, pitch, dynamics, articulation, etc. In order to sound D dorian you have to give emphasis to to the tonic (D), to the minor 3rd (F), and most importantly to the major 6th (B) which is the characteristic tone of the dorian mode. In other words, you emphasize the important chord tones of the Dm6 chord, and play other more as passing tones. Similarly, to sound G mixolydian, you have to emphasize the tonic (G), the major 3rd (B), and the minor 7th (F), which is the characteristic tone of the mixolydian mode; those are the important chord tones of G7.
Once your playing revolves around the chord tones, the other tones you play as passing tones (or other kind of ornamentation) can be either the diatonic tones of the mode, or some non-diatonic tones (which amounts to play some altered version of the chord), or chromatic tones, etc. depending on the "color" you like to give to your playing. In any case, this remains tonal playing (from the point of view of harmony), as opposed to the kind of modal playing you would do on So What.