When your heat pump is using emergency heat yes it'd be "better" to burn natural gas to do so directly that to burn gas to make electricity to do resistive heat

When your heat pump is using emergency heat yes it'd be "better" to burn natural gas to do so directly that to burn gas to make electricity to do resistive heating. However you need to look more at the average scenario to draw a complete picture. When your heat pump isn't in emergency heating then it's more efficient to burn the gas for electricity to power that heat pump than it is to burn the gas for heat (moving heat is substantially cheaper than making heat). So how often is your heat pump in regular heating vs. emergency heat? And then is it in emergency heating often enough to justify having a secondary piece of infrastructure to get gas to your house where you then also need a gas furnace which is more expensive than some resistive heat strips are?