Heat pumps can be cheaper than gas boilers to operate in many locations. It depends on the local cost of gas per therm, the local cost of electricity, the climate, and the heat pump's capabilities.
For example, if you have a heat pump with an average COP of 3 for your climate, the heat pump will be cost effective as long as the total cost of electricity per therm is less than three times the total cost of gas per therm. The hard part is figuring out the average COP and the costs of energy in comparable terms.
Note that Fujitsu's mini splits won't work below 14F. If you want to use mini splits for your only heat source, you should be looking at Mitsubishi or Daikin equipment. Mitsubishi has the best low temperature performance on the market right now and Daikin makes an air to water heat pump that can drive low temperature radiators.