The oil companies will have a very good idea that trouble is brewing. Their aviation advisors watch this forum so whatever is said here they will be taking notes. Their poker faces will be saying problem bilong contractor, but behind the scenes a plan B will have been formulated. I have no idea whether Bristow will have briefed them on the situation, it would be in their interest too.
The oil companies might only be interested in the bottom line when it comes to contracted aviation, but they are savvy enough to realize that helicopters not flying costs them a hell of a lot more than helicopters flying. When reacting to an industrial situation, their response will be to pump the aviation budget down the sludge pipe and throw the resources of their very deep pockets at plan B.
None of this extra money will end up in the pockets of those who decide to tools down. I hope they get their 747 pilot salary or whatever it is they seek, but I suspect they won't be getting a dime more than they get now if they do decide to take action. But someone else will, because collective solidarity amongst pilots has always been weak and the offer of strike breaking money will see enough crossing the line to keep the helicopters flying.
It will be very interesting to see how things pan out.