Maybe. The plants are expensive, the last round of proposals and bids centered around $6 billion dollars to construct a nuclear plant. That's a lot of money. Such a plant would produce 1000 Megawatts of electricity.
If the plant was financed with 20 year bonds, bearing 6% interest, the yearly bond payment would be $480 million dollars. That's the payment to the bank every year to pay off the bonds. That's also a lot of money. Will the plant sell enough electricity to pay its mortgage?
Assume the plant runs at full load 24 hours a day, 365 days a year. Assume they get 8 cents a kilowatt hour for their juice. Then the plant makes $700 million and some change a year from sale of electricity. Subtract the $480 million mortgage payment and the owners have a yearly cash flow of $220 million to pay the workers, purchase fuel, keep the plant up, pay their taxes, pay off the lawsuits, and provide some profit.
If any of the assumptions (interest rate, electric rate, demand for all the plant's output all day long) change for the worse, the plant may start losing money. I hear in the Journal that banks are unenthusiastic about lending for nuclear plants for fear they may default on the loans. There has been demand for federal loan guarantees for nuclear construction.
One thing that would help is reducing the cost of the plant. A lot of that $6 billion goes for permits and review of the design and getting Nuclear Regulatory Commission (NRC) approval of the plant design. And fighting the greenie lawsuits. These costs could be reduced by coming up with a standard design to eliminate the NRC review costs. Plus legislation to reduce the grounds for greenie lawsuits.
Bottom line. Nuclear power ought to pay for itself, but the margin of profit could be wider than it is.