There's nothing you're going to pick up by osmosis. If you need to concentrate on something else, then you're not going to be able to concentrate on anything musical. The best thing you can work on if you can't have your instrument in your hands is ear training; if you have any commute time you can work on singing intervals, triads, 4 part chords. You can make a CD or file of intervals, triads, chords on a piano ro keyboard to work on identification and singing. You can have a recording of lines and solos at halftime to learn to sing those, once you have the instrument in your hands, you just play the notes you can sing.
Listening to a metronome click while you're doing something else is about the most useless thing you can do. Solidifying your timefeel is about awareness of how it FEELS when you are playing against a rhythmic constant. Not about trying to "memorize" a metronome setting.
But ALL of this demands your attention and concentration. If your job demands that too, then you aren't doing yourself any favors in either endeavor by trying to split your attention. Use your breaks, your lunch time, your commute, the ride up in the elevator, but put your self entirely into the exercise.