Do you have the Network Analyst extension?
Do you need to 'weight' physical distance to account for travel time? (some roads are H* in the morning)
Is everyone driving? or is public transportation an issue?
A quick estimate would to produce a convex hull around the point address locations and find the 'centroid' of the Hull.
This would be a Euclidean estimate and not a road-based one, but it might get you ballpark-ish
Minimum Bounding Geometry—Data Management toolbox | ArcGIS Desktop