No, not really. In a war footing, the power plants themselves would likely be targets; the cables are fairly irrelevant. This sort of interconnect lets spikes in consumer demand get smoothed out.

The cables are extremely relevant: it is far harder to protect hundreds of kilometres of underwater cable, of which any part can be cut by a difficult to detect submarine, than it is to protect power plants.

No there's really no way to protect civilian power plants against modern stand-off weapons. It's just impractical at any reasonable cost.

There is no such thing as a perfect defence, against an enemy with unlimited resources. But it is much more expensive to attack an enemy's power plants with $1 million cruise missiles than it is to cut their underwater cables by dragging anchors over them. Also, you can plant bombs on underwater power lines and set them off later - that's a huge problem re: how much energy capacity could go down at once.

Anyway, we definitely can protect installations from stand-off weapons: CIWS systems like the Phalanx can shoot them down these days, and they're relatively cheap. It's not perfect protection - eventually one will get through - but it does raise the cost of a successful attack substantially.

The cables aren't critical, though. They're nice to have for peacetime, but given it hasn't happened yet it's clear each nation is able to at least function without them. In a war, there'll be bigger concerns than "everyone turned on their AC in Israel and we'd like to buy energy from Greece".

One of the biggest goals of the many undersea cable projects around the world is to enable much higher dependence on unreliable renewable power. They may not be critical yet. But they will be.

It, and any kind of infrastructure, would be a prime target - assuming that is what they want. But infrastructure represents value, destroying a country's powergrid and connections like that is only a thing if your aim is complete destruction.

Ideally, in war, you destroy their military, or at least damage it enough for the other party to concede and discuss peace terms, and leave the rest alone.

WW2 was, I believe, the last war where they went for complete destruction of infrastructure, industry, and civilians. The Allies firebombed Dresden and nuked Hiroshima and Nagasaki. It is estimated that 50-55 million civilians died in WW2, of which part due to disease and famine. No conflict since has had that high a civilian casualty rate.