Hi alan_v!
Although vacuum bleeding certainly does make bleeding the cooling system a much easier project, generally in most cases no, you should not need by necessity to remove trapped air.
Usually this is for when there is a bubble trapped deep within the system. Sometimes with pesky bubbles like that you can get away with jacking up the front of the vehicle and letting it sit overnight with the cap and bleeder screw off.
Anytime you disturb the cooling system it needs to be properly bleed so you're best off replacing the temp sensor and thermostat at the same time and then bleeding the system after.
It's great you have a Bentley manuals as those are an awesome resource for trusted information. Also check ou our DIY article on the subject. If you scroll down to figure 8 you will find some tips:
https://www.pelicanparts.com/techarticles/MINI_R56/56-WATER-Draining_Filling_Cooling_System/56-WATER-Draining_Filling_Cooling_System.htm
-Matt