Not with a push/pull, no, it works as one or the other and can't 'hold' setting once switched.

If you want volume and tone and to have the settings 'stay' in a single control your only practical option is a concentric pot. That would allow you to control both volume and tone but requires a stacked knob that typically has limited styles, so that option will depend on the style of knobs you want to use with the build.

Like I said it depends on how you want to incorporate it into the rest of your circuit as to what the best options would be.