Do emergency services helicopters fly VFR when leaving base?
If the helicopter is operating at an airport, it needs clearance like a regular flight, otherwise it would be a very dangerous situation for the helicopter and any other traffic in the area. Usually the ATC will give priority to the emergency helicopter (as much as possible), so it will leave the area without delay.

Regarding the weather conditions, there are two aspects that need to be considered:


The regulations allow emergency helicopters to fly VFR below VMC minima (this is true in Europe, I have no idea about FAA). So, an emergency helicopter, can continue VFR with visibility down to 1km, or even 800 meters for short periods of time.
If the helicopter is IFR equipped and the pilot(s) IFR rated, it can switch to IFR if necessary. On the way to the accident site this might not be very useful if the weather will not allow safe descent and switch to VFR, but on the way back to the airport/hospital, it can be very useful, provided the landing site has some kind of IFR procedure. Again, ATC will usually offer full cooperation in all this switching of plans and flight rules.