no, the MX 1604 doesn't have inserts. You have to go farther up the Behringer scale to get a mixer with inserts. I have the Yamaha MG16/4 and it does...
Sorry, don't know much about patch bays, other than to know that it sounds like that is waht you need. Basically, it means you can plug something into input A and get one or more outputs from that signal.
Or, like has been suggested, a new mixer that does have inserts (which can serve as direct outs). Like my Yamaha board, I can get 14 discrete output signals: 8 from inserts, 2 in the main, two in the alternate bus, and two in the aux sends.