Broadband (aka Internet access) is closer in concept to the wires that bring you the power than the power itself. So to a simple approximation, no.
But it is more complex than that. Like famous quote, the Internet does in many ways function like a lot of tubes. (The Intertubes
) In this way it is a lot more like the water supply. Your ability to get water out of the water supply is restricted by the diameter of pipe you have coming from the water main. But only up to a point. If you have a pipe to the main that is as big as the main, or even bigger, you won’t get any additional water flow, and you will be restricted by the diameter of the pipes feeding your part of the supply network.
Similarly, your broadband access is already restricted. You share access to the Internet with all the other people in the street. Just as if everyone in the street turned on taps in their houses simultaneously, and noticed that the water pressure was low and the flow poor, if everyone in your street tried to stream movies at once, they would discover that the bandwidth was not as good. This comes about, in part because of the way each connection in the street interferes with one another, and in part because the upstream feed does not have the capacity to feed every single downstream feed at full speed. Telcos and ISPs try to balance things so that (just like the water supply) they don’t have to provision the network to the full sum of all possible simultaneous use.
Then of course, the big difference between Internet, water and electricity, is that there is no small number of very large suppliers of data for you to access. Not like a few reservoirs or a few power plants. There are millions. Some are very large and have entire data centres devoted to providing capacity, some are tiny and may be supplied from something as tiny as a mini-pc in someone’s home. In the new-fangled internet of things, you might be accessing a multitude tiny devices no more complex than a light bulb. If lots of people try to access the same supplier of content at once, that supplier could become overwhelmed. (eg the slashdot effect)
In the middle of this your ISP, and their upstream suppliers (the major long haul data carriers) all try to balance an ability to supply data versus the cost of building bandwidth. One thing that has allowed them to keep pace with the exponential growth of the Internet is that fibre optic cables are not a limitation to bandwidth. They are like having infinitely wide pipes in the ground. The only thing you have to do is work out how to pump water down them. So as electro-optical technology improves, all the carriers need to do is swap out the equipment at each end of a fibre backbone, and get ever more capacity out of the same length of optical fibre. The fibre cost a lot of money to lay, especially all those trans-oceanic links, so they get a massive boost in capacity for relatively not a lot of money (relatively - a termination unit can cost six to seven figures.)
So, rationing in the form of actual loss of connectivity isn’t what you will (or do) see. Now and into the future, what you will see is a lowering of performance as different parts of the network become saturated. Saturation can occur almost anywhere in the end-to-end link. Much more like the water pressure going bad than the electricity going off. (The electricity goes off because it isn’t possible to reduce the pressure - aka the voltage - as whilst your lights would just go dim, most other equipment can’t function unless it receives the designed voltage and power. So the power is shut off in rotation to ration it. Electricity supply is unusual in this respect.)