Can you send data to a server through cellular?

Hello all. At my current job we have sensors on one of our building’s roofs that sends environmental data from the roof to a physical server in the building. This system is proprietary and our building does not allow WiFi, so we are seeking a way to store this data through a cellular network (or other means that aren’t WiFi). We are currently considering using an Arduino cellular shield to send the data, but are not sure if data could be sent that way with Digital Ocean’s servers. My team and I are new to Digital Ocean and haven’t really worked on a task like this, so any and all help is appreciated. Basically, we’d like to be able to send the sensor data to the roof via cellular, but also be able to get updates on the data (most likely through SMS with the Arduino shield). We have a couple guys (including myself), that are familiar with C++, so I don’t think that coding will be an issue. Thanks in advance.