I don't think this would be good for the character, the way she's portrayed in the movies.
One thing that I like about movie Pepper is that she can be intelligent and strong in some ways, while still being a little "girly." She's an equal partner to Tony in their relationship, and she's the more sensible and responsible one who can call him on his crap. But she can still get flustered and display vulnerability.
Something that stood out to me in Iron Man 2
was how she contrasted with Natasha Romanoff. When the two of them confronted Justin Hammer, Pepper talked tough without sounding "tough." She was willing to call the cops, but she was shocked when Natasha got physical.
I love both of them as characters, and it's nice to have that kind of contrast. The last thing I want for this character is for her to turn into another ass-kicking Action Girl.
Also, "Rescue" is a pretty cheesy name.