All the officers are potentially action characters because they are trained officers. The trick is using them in scenarios where they are useful and not shoe-horning them in.. So no, Uhura should not be sent on a mission instead of security staff (unless as the officer in charge) but yes, she should be sent on a mission where her skills (computer expertise and fluent Romulan) might be of vital importance.
I'm also an advocate of Janice Rand being given some air time. She could well be Kirk's Yeoman and would therefore have a reason to accompany him on missions but give her security training as well and she becomes a potential action character. They've done this in the comics, although at the moment we've never seen Rand actually function as Kirk's Yeoman so their close relationship from TOS has yet to develop.
McCoy will always have a reason to be there since every away team needs a medic e.g. if Pike is injured. I think they missed a trick to use all four characters on the Narada.