How critical is to keep this contact for an organist?
I think it's important for at least two reasons:
1. It's vital for the control of releases of notes which is the key to achieving the desired and precise articulation.
2. The pipes can speak to the best of their ability.
The first point is extremly evident when you play polyphonically complex music, such as the Baroque pieces. Because of the intensity of independent melodies, each voice requires its own articulation which is best controlled by keeping the contact with the keyboards and pedalboard. It's also important even in the Romantic and modern organ music when some notes have to be shortened to the exact point.
The second point is most applicable when the tempo of the composition is fast and when there is a need to play staccato. Lifting off the fingers and the feet into the air often makes the staccato sound too short - the pipes simply don't have enough time to speak.
If you have an extensive training in piano playing, keeping contact on the organ is not easy. It's a new habit and as always, forming a new habit requires time, patience and some perseverance but it''s definitely makes the playing much more idiomatic on the organ.