scouser, the short answer is yes, it will "work" BUT you need to carefully acquire the correct components AND connect them correctly.
You may know this, but . . . From your description, its not clear if have a gas valve that is modulating or a shutoff. A modulating valve would require an input signal (4-20 mA is most common but not unique). A shutoff would require use of the relay outputs to energize/de-energize for controlling the temperature. Both controllers seem to have both types of control, so order and configure to your setup.
You asked about what type of probe to use. The thermocouple you mentioned is the actual probe. Regardless of what type of probe you use make sure the controller hardware (I/O card) is the same type. The instructions don't mention it, but also do NOT connect the thermocouple to the controller using regular wire. Thermocouples require "thermocouple extension" cable. They are color coded to help avoid errors, make sure both wires in the cable are the same as the thermocouple's.
IMO, this will work best if you get the temperature measurement measurement inside the mashtun. And since you are going to some effort here . . .
I may have got off-topic, but hope this helps.