Can a driver expect to see pedestrians using the full width of the road beyond this "residential area" sign?

In the video you are entering a narrow street in a small town; on the right there is a blue sign D-40 "residential area", and below it sign B-18 "3.5 t". Beyond this sign you can expect pedestrians using the whole width of the road. The answer is: yes.

The Regulation on road signs and signals states that sign D-40 "residential area" marks the entry to a residential area, and the Road Traffic Act adds that the usual rules for pedestrian traffic do not apply in a residential area: a pedestrian uses the whole width of the road and has right of way over a vehicle. This means that beyond sign D-40 people may walk in the middle of the roadway, children may play on it, and you drive at no more than 20 km/h and give way to them, even if there is no pedestrian crossing there. The sign also informs that speed bumps and other devices forcing slow driving might not be marked with warning signs, and parking is allowed only in designated places. When leaving the area, you are joining traffic (włączanie się do ruchu) and give way to everyone. Sign B-18 below it prohibits entry to vehicles with an actual total mass of more than 3.5 t.

Legal basis: § 58 para. 1 and 2 of the Regulation on road signs and signals; Art. 11 para. 5, Art. 20 para. 2, Art. 17 para. 1 point 1 and Art. 49 para. 2 point 4 of the Road Traffic Act (Prawo o ruchu drogowym)