I can attest that I'm in awful shape—I live a sedentary lifestyle, walking to school and back and that's about it—but when I wear maybe 70 lbs. of platemail, I can most definitely run. No, not as fast as normal, but still a definite run (I could certainly outrun anyone trying to run backwards). The main difference is that I tire very quickly. If I wore it enough, I have no doubt that I'd tire a lot less—still faster than if I weren't wearing it, of course, but not that fast. The main problems with full plate were that a) it was hideously expensive, and b) it became near-obsolete after gunpowder became really prominent.
-Simetrical