Thoughts on furnace generator transfer switch install
You said inverter generator , these are usually much better than the type I use, with the old fashion alternator and voltage control. I power my TV’s and microwave refrigerator, furnace  and well pump with mine and have done this for over 20 years without knowingly killing anything. 
I have been on generator power up to 2 weeks and loose power for at least a day every year usually several. 

The important part is not overloading your generator , I usually am well below the generators rating and maybe close to 1/2 of its peak rating. 

The reason this makes a difference is because when generators are over loaded they start surging this causes the frequency to bounce and the voltage to spike then droop. With a proper size for the load the generator will only vary slightly. 

Your inverter rating is 2kw but what is the load the boiler needs (the pump being the big draw of the system) if your recirculating pump is a fractional horse power you would probably be fine, setting up a transfer switch for this one unit may be a good idea but I would want a quality heavy duty extension cord 50’ is not that long but pump’s have a large starting current and a small extension cord can increase voltage drop , create excessive heat in the wires and damage the system where a Quality 12 gauge cord will be fine. 

I would move forward with your plan it looks sound and may provide comfort when all else is dark.