I doubt Stevie boy will let it use LTE, but you're right about Verizons networkVerizon's network should be just fine.
They've been handling mass amounts of 3G corporate laptop access for years.
Of course, an LTE-4G iPhone wouldn't use up EVDO 3G resources.
If the iPhone was still 3G-only, the most that would happen is a data slowdown at times. Remember, voice and data are kept separate, which is why there's no simultanous usage, but also prevents related dropped calls such as happens on ATT with UMTS-3G.