Can playing guitar be considered therapeutic in recovering from a mildly displaced 4th metacarpal without surgery?

Depends: It depends which hand the displacement is on, and how you're using that hand. Could over-stress the hand that's doing the chords -- plus be pretty painful. You might speak with a hand surgeon or a physical therapist about your specific injury, and best ways to rehabilitate it.

Yes: Motion and dexterity will help your rehab.

Depends on age of Fx: If its less than 3 weeks, then its best you don't; as i think you might cause it to get displaced. After 5 week yes it'll help, as by then the fx has healed. Between 3-5 maybe, depending upon the fx type, degree of displacement on xrays, etc. Your treating doc would be in a better position to gauge your treatment.