No, I don't think it's that simple. The following is true for Sprint, and I suspect for Verizon also:
The phone will only connect, and stay connected, to 4G if the 4G signal reaches a certain level (signal strength). Below that, it will default to 3G even if a weak 4G signal exists. There is a way to force the device to LTE only, but then it is truly LTE only. No 3G when LTE doesn't exist, and no telephone calls or SMS. See this post for more detail:
yeah I know theres a 4g signal in my living room but the phone won't stay connected. I can force it to stay on 4g on my thunderbolt but on the sgs3 I'm only getting 4g in the master bedroom, which is better than nothing I guess