Yes, I have a Verizon Network Extender in my house that makes the phone work fine there. I use WiFi mostly, anyways, but when I take a 1/2 hour walk near my house and switch to mobile data for that (3G only, turning off the WiFi, already turned off 4G which is hopeless here), the battery goes down about 4% in that half-hour with no usage. If I were using only 3G all the time, you can see that in my area the phone would only get 12 hours with no usage (essentially on stand-by) because of the low cell strength in my area. If I were using it a lot during that time, I'd estimate maybe 4-6 hours or less between charges. And 4G is even worse, since it is even more marginal here. So yes, weak/marginal signal strength has a radical effect on the amount of time that you can use your phone without having to charge it. According to Verizon, I'm in an excellent signal area for cell phone, 3G and 4G. When I go outside my house, I'm lucky to see 2 bars on my phone, and where I take walks near my house, 1 to 2 bars.
Before this phone, I had an iPhone, same thing. The battery would go down very rapidly when the Network Extender wasn't on for some reason, even in WiFi only mode due to the low cell signal strength. Sucks, but the Network Extender at least makes it reasonable inside my house. Outside I have to go to "airplane mode" until I get to a higher signal strength area or until I absolutely need to use it. And 4G isn't even in the realm of possibility around here (the Network Extender has 3G, no 4G boost).