Considering that BHA have been taking on and training new Co-Pilots over the last few months and are in the process of getting some new aircraft in their fleet I doubt that there will be much movement in Pilot numbers any time soon.
Training up new guys to be multi-engine offshore IFR drivers takes a long time a lot of effort and organisation and BIG dollars. Even IF there were to be a significant downturn then Bristow, CHC etc would be loathed to cut Pilots because when the downturn ends they need to get them back on-line asap. Pilots who are cut loose still need to pay the bills and will have moved on possibly not to return quickly enough or ever?
A downturn in the offshore market would only initially really affect the exploration and drilling sectors of gas and oil. Production is an on-going requirement and will therefore be unlikely to suffer as much.
Guys who are at the 'bottom' of the heap in terms of seniority will of course be a bit 'twitchy' given the level of economic unrest and usual Pilot rumour and speculation. However, rest assured these guys who have the training, endorsements, ratings and even a small amount of offshore experience will be the very first to be picked up when the stock market stops crapping itself!
I guess it's reasonable for others to suggest given the current climate that Bristows or CHC offshore in Oz are going to be laying off Pilots. I haven't heard any such rumour, and NO I'm not on anyones management team!!