As a domestic/residential consumer you'll only be billed for real power (kWh). I've never heard of exceptions anywhere in the world to this.
That being said, copper losses in your local installation (=after the meter) due to bad power factor will of course increase real power consumption a bit (perhaps 1...3%).
Large-scale consumers (office buildings, industry, super markets, shopping malls, server farms) is a different story. They pay for reactive power.