So assume that if a house costs more than a similar house built for natural gas, there's still a payback period.
However if you're starting from scratch, it depends on the upfront capital difference. It gets tricky to compute because a lot of the payback period is going to depend on what local infra you were going to connect to and what it cost to do so in addition to whatever difference there was between thee cost of the in-home appliances, in addition to sunk costs you might have to pay for anyway.
Usually electric water heater is more expensive than a gas one, and the electric water heater's operation cost in electricity is more than the gas one's cost in natural gas.. but if you're putting solar panels on your house that can go the other way.
Running a gas line is likely cheaper than the upfront capital to build out a solar plant, but its not if you're rural in a lot of places.
Also, there's other factors:
If you have really bad asthma or a respiratory disorder not having, not having gas appliances running in your house can cut down on your medical bills.
In the end, it depends on where you draw your system boundaries.