We would have to know what phone you are referring to. Generally speaking Verizon 4G LTE covers everything (data, voice and text/sms). If there is no 4G signal then text wont work either. If your phone can fall back to 3G then maybe, but you need a signal from Verizon one way or another. No signal means no services either.
If you have the option to use WiFi in this location then I would not rely on text/SMS. Instead find a messenger app that works over WiFi such as Kik. Send your messages over WiFi instead of SMS and you should be in business.