No, it's not going to save any money. In contrast, it's going to lose money.
Let me explain. If you buy a fixed price electricity contract, and the price of electricity skyrockets along with the price of Bitcoin. You are lucky to have the old low price. It makes sense to start mining Bitcoin, by increasing your electricity use, because you are paying too low price for the electricity.
If you buy a fixed price electricity contract, and the price of electricity crashes because a new energy-efficient technology generation of electricity-using household appliances has arrived to the market, you still pay the higher price. It makes sense to reduce your electricity use by buying more efficient household appliances, because you are paying too high price for electricity.
Or consider this: if you have the ability to charge your electric car at home and at work, and the workplace charges a hourly market rate for electricity, will you charge at fixed rate at home or at variable rate at work? You will select the cheapest rate, of course.
Your use of electricity does not follow the natural demand curve. If the price of electricity is artificially high (you pay more than it's worth currently), it makes sense to reduce your electricity use, thus deviating from the natural demand curve. If the price of electricity is artificially low (you pay less than it's worth currently), it makes sense to start mining Bitcoin / stop charging your electric car elsewhere and only charge at home.
The electricity company has to take into account this.
Similarly, the natural gas company has to take into account this. For example, if the natural gas price crashes, you still have to pay the old price, thus deviating from the natural demand curve. If the natural gas price skyrockets, you won't reduce your usage, thus deviating from the natural demand curve.
Because consumers can and will adjust their behavior as a function of price, what you're effectively buying is some form of insurance. It's not a futures contract (futures contract would apply if you were FORCED to use a certain amount of electricity / gas), it's an option, since you are not forced to use natural gas or electricity. Options have a price.
The electricity / natural gas company has to pay to the derivatives market to buy those options. Or if the counterparty is the company itself, they have to price the options correctly in their balance sheet, using the Black-Scholes model.
My take? I don't have natural gas where I live, but my electricity contract is based on hourly market price. It's the only sensible choice, even for those who don't follow the hourly market price. It will average out in the long run and be cheaper in the long run.
If I had a risk to insure against (example: electric heating in an old house in very cold climate where annual heating bill exceeds 5000 EUR), I might pay the extra price of a fixed contract.