It depends on the boiler.
I have an old Vaillant VUW240 / 2-5 and there it was possible to mount circulation on the "bare" 2-function boiler.
The boiler has a secondary exchanger, which in both circuits has a capacity of approx. A glass, but also has the COMFORT function, which means that the boiler constantly maintains a certain temperature on the exchanger or you can use the room regulator to heat the "tank" or set the time periods in which is to be hot water heated. One-time heating of water in the container takes about 9-10 liters of gas. With circulation, one-time heating would certainly use more gas but how much exactly I have no idea.
When I had the boiler installed, I had no idea what circulation was, so I did not put it on because of the extra costs, but now I know what a bajer it is and I would certainly install such circulation to my 2-function boiler. Unfortunately, the installation of circulation would mean that I would renovate half of the kitchen, part of the corridor and basically the whole bathroom, so this solution is out of the question.
I have to wait about 0.5 minutes in the shower until they order about 3.5-4 liters of cold water and heat from the boiler. Circulation would increase comfort and reduce water wastage at the expense of slightly higher gas consumption, but on the other hand you would not have to wait for 0.5 minute, during which the boiler works and the gas flies into the chimney, so for a single heating cycle total consumption with circulation could be on a similar level or even a tad smaller.
