Depending on its specific design, the resistor will be able to handle short peaks of power dissipation far above its rated capacity.
With regard to a pulsing supply: that depends on the supply and how it behaves when "turned off". If the supply becomes high impedance in the off state, nothing much will happen as the capacitor just retains the charge (presuming the exact circuit as depicted with no loads other than the series resistor). If the supply is shorted when off (or a load is draining the capacitor), it's a different story - the capacitor will charge when the supply is turned on and discharge when the supply is turned off.
Generally, if the charge time of the capacitor isn't very long, calculating the RMS power dissipation over a single cycle and taking a safety margin of 2x should give you plenty of headroom.