Do you know if it has a 24 volt transformer in the heater? Does it have a wiring diagram? Some of those are millivolt systems. If it's millivolt you will need a wall transformer for 24 volts AC. Let me know and I can tell you how to wire a transformer if you are going to need one.
Yes but if the heater does not provide 24 volts to the existing thermostat then the Nest will not work it needs power on the R and a C common wire to keep it charged up. Some of those shop heaters the power to the thermostat is only very low millivolts not 24 volts. So determine using a mutimeter set to AC volts and test the 2 wires at the existing thermostat see if you get approx 24 volts AC not DC. If no, then set meter to millivots and test again.
What brand and model heater is it? Can you post a pic of it with and show where the existing thermostat wires connect. The only way to know if it will be a standard installation like a house furnace is to see pics of where the thermostat wires connect to the heater to see if there is a terminal for a C common wire to connect.
Yes it can but only if the heater has an internal 24 v transformer that provides 24 Volts otherwise you need to add a separate transformer plugged into a wall outlet to provide constant 24 volts to the Nest R and C terminals, the heater will connect to R and W.
If heater has a way to connect 3 wires R W and C to the heater then you wont need a separate transformer but if it only has the terminals for the 2 existing wires then watch this video. You can buy those transformers on Amazon if you need one for under 20 bucks.
Here is a transformer if you need one