Starve maybe, die of thirst almost certainly.
You are correct, the experiments they are referring to are the series of experiments by James Olds and Peter Milner in the 1950's 60's and 70's that first discovered the pleasure center in The brain and indeed quite possibly the pioneering experiments in behavioral neuroscience.
In specifically this experiment in 197 which was one of the later ones set up to test if the rats were making a choice based on competing stimuli (food, water, mates, pain, pleasure). Remember these are the foundation studies for all of neuroscience that actually begin to show how the brain worked. This particular study set up basically the simplest maze ever (literally a single T) with the trigger for the pleasure electrode in one direction and a series of other things in the other, both visible from the other in a direct line. They could not reach both at the same time but they could always walk from one to the other. Incidentally his is also the one that forced the rats to cross and stand on an electrified grid inducing pain to push the lever.
To be clear rodents and small mammals in general begin to starve quickly, but die of thirst in an absurdly short amount of time. It takes about a week or two for a rat to starve, only a day or two to die of dehydration^. The rats were found to ignore food and water even when seriously deprived of both, seriously deprived in this case meaning more than 24 hours without food and water (both is important for many rodents the bulk of fluid intake is from food) as long as they had to choose between drinking/eating and electrical stimulation. More importantly no deviation from this pattern was observed no matter how deprived the animals were. Even when the current was removed the rats instead simply laid down were they were and went to sleep rather than seeking easily available food or water. The animals were really in no risk of starvation but were in serious risk of death by dehydration, this is the equivalent of a human going 5-7 days without water, and they still would not stop pushing the lever to get to water that was literally a few feet away.
For ethical reason the animals were eventually fed and watered because the conclusion was they would continue to prioritize stimulation until they died. For similar ethical reasons these experiments were never carried to this end, as it really would not have yielded useful information. Another likely consideration was the surgery was not easy, the whole discovery of the pleasure center of the brain started because hitting a specific portion of a rate brain with the wire was difficult and they hit the wrong spot, so killing the rats would be pointlessly wasteful as well.
Were the animals allowed to die, no, but scientist had and still have every reason to believe they would die if the experiment continued, and they reported as such. You don't have to kill an animal to reasonably believe it will die. The Rats were seriously deprived and still ignored food and water, the conclusions was a certain as reasonable ethics would allow. The rats showed a disturbing lack of interest in other stimulus in general once they acclimated to the pleasure electrode. From modern studies we know the brain becomes increasingly resistant to all stimulus when it becomes acclimated to a super stimulus. The brain basically develops higher pleasure and pain thresholds.
because link stability is an issue the experiment is
Kornblith, C., & Olds, J. (1968). T-maze learning with one trial per day using brain stimulation reinforcement. Journal of Comparative and Physiological Psychology, 66(2), 488-491.
Other linked studies
^Mammals in general are very inefficient with water. Mammals deprived of both food and water dehydrate even faster as the bulk of our water intake is in our food.