Probably not .... I certainly don't.
The introduction to the film is just as important (often more so in some cases) as any other scene in the film. I cannot see how lopping off the first twenty minutes makes the film 'sharper' if what you have done has made no significant impact on the rest of the film. Also, why the necessity for it to make 'quicker sense', for me part of watching a film is to see events unfold and see how the characters react to them. To simply drop Johnson into the situation is to take him out of his personal context, thus robbing the viewer of seeing possible character motivations that might have been subtley placed in the introduction by Val Guest.
It's a bit like taking the scenes of Insp Martineau's home life and the backstory with Don Starling out of
Hell Is A City, or removing the introductory scenes in the house from
Jigsaw. It wouldn't disrupt the plot too significantly but would lessen the viewer's knowledge of the characters and their context therefore reducing their enjoyment of the film
Bats.