This seems like a normal scenario that we have in here. We have 2 VFR Chopper routres that run east/west 2NM north and South of the runways OM position. Traffic on these routes are deemed seperated from the dep/arr tfc but ussually a TCAS warning will be received by the acft. Traffic info is not ussually given to dep/arr flights unless the flinging deviates from the published route as flight crews are expected to know that choppers could pass below them on these routes as it is published in our AIP. I ussually pass tfc info anyway just to avoid the paperwork if an acft reports a TCAS warning, although our SOP's state that TCAS should be turned off in the TMA and CTR. (Our Company requires us to file a report for all TCAS warnings if the pilot reports such warning on Freq even if std seperation was maintained.) Most Airlines who operate here keep there TCAS on at all times in flight.
As PIC I feel that you may refuse dep if you wish with the chopper in the climb out path as you have final responsibilty for the flight (this will usually envolve some choice words from the ATC before they key the mike again- Take notes on how to **** an ATC off in 1 easy step.) In most cases here unless the helicopter if medical or police the helicopter will be instructed to move for your dep if you refuse to depart however we seldom get a refusal to depart.