Captain America will actually be a lot of help (as will his forces). I'm going to just address things as they occur to me and I haven't confirmed these things with the co mod/my partner in plotting but here they are.
1) The "Panic in the streets" thing I think is going to be basically something triggers a wave of mass hysteria among humans (or something of that ilk) those who've been trained to deal with panic and terror (like say the initiative) won't be immune so much as they'll know how to take a few deep breaths, get a good hold of themselves, and function. They'll be highly useful trying to retain some kind of order when everyone is crazy.
2) The eleventh (and for that matter the 12th seal as well) are broken upon the deaths of certain people. While these people are relatively safe within the walls of Wolfram and Hart (and not exactly helpless) there is the issue that Wolf Ram and Hart are behind the effort to kill them. Having a platoon of special forces who haven’t sold their souls to the senior partners acting as body guards might be helpful keeping said people alive.
3) Once the eleventh seal is broken there will be three days before the armies of heaven burst forth to turn the tide. I kind of imagine the three days in the mean time would be a wonderful for Riley and his troops to have a crowning moment of awesome as they struggle against overwhelming odds to just keep as many people as they can *Alive* through those three days (maybe they've formed a "Safe zone" and try to protect it while bringing people into it) so when the armies of heaven come to the rescue there will still be people in the city of angels alive to be rescued.
As for the initiative working to retrieve artifacts Eliot's job until enough slayers alive to make a class (and even after that) is organizing retrievals of said objects using his contacts in the criminal underworld and either hiring people he trusts or doing the retrievals himself (that sentence probably makes a lot more sense if you've ever seen Leverage but if you havn't before coming to LA to save the world retrieving heavily guarded objects/people was what he did for a living). But maybe they can work together?
Even if Eliot hasn't been in the military officially he's done enough work for and with them (and fought in at least one war) that he'd probably get along pretty well with Riley. Eliot's less the war tactics big picture guy (his focus is more on defense, training the slayers, and protecting the head honchos) but he could probably find plenty of areas to talk with Riley about.