I can't say for certain whether or not suicides were... prevalent but the stress culture associated with the GaoKao is NOT anything new. Suicide is a MASSIVE taboo to Confucian scholars in most contexts, so I'm not too sure how the strict social norms influenced personal behavior in the context of the examination culture. Your question is certainly one that deserves more in-depth research, which I cannot provide as I am a largely illiterate pleb. There were certainly stories inspired by the immense pressure to succeed in the examinations and we have many artifacts from the time period which point out the sheer desperation of some examination candidates. I hope you don't mind if I broaden your question a bit to 'Was examination stress culture prevalent?', and then attempt to provide an answer.

Within Cao Xueqin's famous Dream of the Red Chamber, one of the main characters is Jia Baoyu who is extremely negatively affected by his strict, Confucian scholar-official father and he is both apprehensive and put-off by the civil service system, pointing to the extremely uncomfortable social position that sons of men of learning were put in. They were expected to succeed both for the honor of the family and for a chance to advance the social standing of their clan. In Liaozhai Zhiyi, or Strange Tales from a Chinese Studio, a famous collection of some 500 short stories written by Pu Songling, there is one story contained within the anthology that describes a young scholar's unsuccessful attempts at taking the metropolitan exams in the capital. He returns to his home, heartbroken from his failures and quickly falls gravely ill and perishes. Then his corpse/zombie/ghost/spirit thing wanders back into the capital to retake the metropolitan exam, which he passes, but upon his return, his wife points out to him that he has long since died, at which point his spirit vanishes into thin air. Quite bizarre, I know. Pu Songling himself was born into a gentry family that had fallen onto hard times, and he was a repeatedly unsuccessful candidate for the Gongsheng degree, or the Provincial-level exams. As a result, he grew rather disillusioned with the entire system, not unlike many other disgruntled scholars from both the Ming and the Qing, where the examination was extremely competitive. That shit makes the bar exam look like a walk in the park. Pu Songling's story is one that emphasizes the sort of intense nature of the late Imperial Chinese examination system. Both men write of an unforgiving system for those unfortunate enough to pass through them as failures.

There is even a deity in Chinese mythology known as Zhong Kui who ascended to divine status after he killed himself because he was stripped of his Jinshi degree. So yeah... exam stress culture was intense.

As a way to better illustrate the stress culture, we can just briefly take a look at the extremes some individuals took to try and succeed; candidates became ever increasingly more creative in their methods used to attain a passing score through cheating. Due to the strictly enforced structure of the exam system and the rigourous curriculum of neo-Confucian orthodoxy of the exam itself, candidates were required to recite, verbatim, many thousands of passages and phrases from the Confucian classics. This requirement of rote memorization led to the creation of many so-called 'cribbing garments'. Much like a cribbing sheet, answers and other illicit materials were written onto the base material, but these garments were literally worn by candidates into the exam halls. There are even examples of undergarments being used to facilitate in the rampant cheating going on, with literally the equivalent of entire pages of Analects copied onto them in near-illegibly small handwriting.