Since natural sciences are about experimentation...
Let's mutilate my poor old 2010 model 25MHz Pico with 5ns riser from Arduino.
2205 does not have true DC offset much like DS1000Z AFAIK.
+-5V (1V/div), AC coupling, 4GS/s ETS, 5ns/div
DC average: -402mV s.d. 2.61mV
Rise time: 9.06ns s.d. 104.3ps
+-10V (2V/div), DC coupling, 4GS/s ETS, 5ns/div
DC average: 2.096V s.d. 4.651mV
Rise time: 9.239ns s.d. 103.6ps
+-5V (1V/div), AC coupling, 900MS/s ETS, 1us/div
DC average: 3.474mV s.d. 2.043mV
Rise time: 9.097ns s.d. 547.3ps
+-10V (2V/div), DC coupling, 900MS/s ETS, 1 us/div
DC average: 2.514V s.d. 2.142mV
Rise time 9.248ns s.d. 540.6ps
Note waveform general look and placement on screen is same AC vs DC mode = controls were operated correctly.
I can see lost precision (look s.d.) due to less vertical bits in "simulated DC offset mode" and DC values are seriously affected in small timebases (=zoom from large timebase on DS1000Z due to screen buffer based processing).