In this scenario, can you enter the level crossing without first checking that no rail vehicle is approaching?

In the video you are approaching a level crossing with half-barriers; the barrier arms are raised, the signal is off, and the road beyond the crossing is clear. Even so, you cannot drive onto the crossing without making sure that no rail vehicle is approaching. The answer is: no.

The Road Traffic Act states that the driver of a vehicle, when approaching a level crossing and when driving across it, is obliged to exercise particular caution, and before driving onto the tracks - to make sure that no rail vehicle is approaching. The obligation is unconditional and applies to every level crossing, regardless of how it is protected. Raised half-barriers and a dark signal only tell you that the automatic system has not detected a train at this moment, but the automatic system may be faulty, switched off for repair, or it may start working just when you are already at the tracks - the red light may come on a second after you looked at it. That is why before every level crossing you slow down, look left and right along the tracks, and when visibility is limited, you open the window slightly and listen. It takes two seconds, and it protects you against a collision that you cannot survive.

Legal basis: Art. 28 para. 1 of the Road Traffic Act (Prawo o ruchu drogowym)