120V and 240V outlet in same box
Yes, 120V and 240V can cohabitate.  Both of those are classified as Class 1 circuits.  The highest voltage present in the box will be 240V, and with any normal wiring (NM, THHN in conduit, MC, etc.) all the wiring will have insulation rated well above that voltage.  

However, depending on the plug on your charger, it may not fit in half a 2-gang.