Excess capacity in the power grid
The short answer is no. There is not "potential" electrical energy present on a power line. Instead, the power company generators are always being tweaked to produce the power needed.

Think of your car doing 55 on a level highway. Now think what happens when you reach a hill and start climbing. With the throttle at a fixed setting, the engine speed will slow down and the vehicle speed as well. In order to maintain a constant speed (and constant motor rpm) you must increase the throttle, and in the process will burn more gas.

Similarly, a generator being driven by a turbine will put out a certain amount of power. If the load increases, either the generator must be driven harder, which takes more fuel, or the output voltage and line frequency will drop. Neither of the latter is considered a good thing. The power grid is obligated to work at a certain voltage (within an acceptable range) and at a certain frequency (50 or 60 Hz). To do this, the generators on the grid are constantly being adjusted. The good news on this front is that, with a large number of customers, the law of averages suggests that for the most part the total load doesn't change very quickly, so maintaining constant voltage and frequency is usually possible.

Just as your car does not usually put out its rated power, so a power grid is not usually driven at full power, and this is where the percentage of capacity comes in. if the grid is running at 50% of capacity, there is not another 50% magically available. Rather, if the load demand doubles, the generators will be able to be cranked up to 100% of their rated output to meet the demand, but this is not instantaneous, and if the power company does not increase the throttle setting on the generators the line voltage and frequency will drop. If the demand gets too great, such as can happen in hot weather due to air conditioners being used, it can be necessary to reduce line voltage ("brown out") or even cut of power to part of the grid, as happens in a rolling blackout.