When does the airline check if an airplane can reach its destination?
The spec-sheet range is not a fixed value—


The range of the RJ85 (BAe 146-200) is 1,570 NM with standard fuel capacity.
Range values are only valid for certain (marketable) payload/fuel levels.
If you have less payload and/or more fuel, you increase the range. Example here.
If there is tailwind, the [air] distance to destination is reduced (apparent range is increased). That's why marketed range circles are not circles, as shown below. Example here.



  The wind may provide a head- or tailwind component, which in turn will increase or decrease the fuel consumption by increasing or decreasing the air distance to be flown.— Wikipedia


Corrected distance (after the average-wind is taken into consideration) is checked in the flight planning phase, and the plane is loaded accordingly (fuel and payload). If the aircraft can't reduce the payload to reach its destination, then a technical stop to refuel is planned.

Google Flights shows all the airlines stopping at least once on the way.



(Source) Range circles take into account the trade winds.