Heli Cal. Yes a distraction like that may well have contributed to the accident.
A small helicopter such as the EC145 is no place to cope with a birth particularly as it appears the doctor was the sole medical crew member. Had it been a difficult birth the combination of the mothers screams and the harrassed doctor possibly asking the pilots to get to the hospital asap would have created considerable stress in the cockpit.
I experienced a similar situation in a SPIFR Bell 412. I elected to carry out an ILS due to the weather being marginal which added about 15 mins to the flight. The baby died and although I think I made the right decision it is still something I think about years later.