Let's take a wild stab at calculating this.
Any calculation would rely on assumptions. Changing assumptions would change the result. E. g. we don't know how much would 1 btc cost in dollars.
I suggest a simpler proof:
1. In the long term Bitcoin mining with ASICs should be profitable (in mature market it should probably give few percents a year).
2. If mining is profitable for mining companies (that pay rent, salaries, etc), then for households it should be profitable too. Or at least cover the energy.
When hardware matures, energy costs for professional miners should be comparable with one for households. Maybe households would have advantage because they don't have much collateral expenses and the heat could be a desired feature, no need to spend energy on cooling