If configured properly, I'm sure it will. We have installed 19 of these (Honeywell Wi-Fi 7-Day Programmable Thermostat (RTH6580WF), Requires C Wire, Works with Alexa) at our church and they work extremely well from the cell phone app. The RTH6580WF are now compatible with the Echo dot, but we have not yet learned that skill.
With two of these T5's at home, they work amazing with the Echo dot and the phone app. They even have geo-fencing option to detect when you get to be within a certain radius or when you leave the building.