Sounds like he could be pretty good for managing such things, yeah. Edgeworth's used to directing investigations himself and might chafe at losing that control, but if Minato proved competent enough he'd adjust.

Another possible role that pops to mind when it comes to many of the skills you list would be a judge, if he's a quick enough study and could be firm enough to keep the likes of Edgey here in line. -- Pteryx