Well, the common-est view is that Qin's advantages were so extensive compared with the other states that their death was only a matter of time. Qin had the advantage of a very developed bureaucratic system (almost totalitarian in its nature, as witnessed at Changping with everybody over 15 in a county being sent to war) due to Shang Yang, Fan Ju and Li Si's reforms. Qin, unlike the other powers, was a state that could draw on large regional resources (the Sichuan Basin, as well as the Wei River Valley) without fear of attack from another front. Qin was also helped by the fact that it had no comparable enemies, it having crushed Wei, Zhao and Chu while a combined coalition practically destroyed Qi.
Jing Ke's assassination occurred around 227BC; this would mean that Qin Shi Huang was 33 at the time. Considering ancient royal practices it's not unlikely that Qin Shi Huang would, by that time, have a son around 16 years or older; mature enough to take power. Of course the fact that Qin Shi Huang's OTL successors were actually his 17th or 18th sons (which would make them aged around 2 or 3 in 227BC) could mean that most of Qin Shi Huang's offspring died relatively early - so in that case, if Qin Shi Huang dies then Qin would be in a right mess. Li Si might still be able to steady the ship, but there's only so much he can do before the Qin royal family/Qin bureaucracy start intriguing. The remnants of early conspiracies - Lao Ai, Zhao Ji, Lu Buwei and Lady Huayang - are still out there, and they will want their power back.
I personally think the character of Qin Shi Huang is relatively important in driving the Qin unification of China, so without him I think we'd see massive and unpredictable butterflies, especially if we consider the poor historical record on the people most likely to succeed him. Those who think otherwise can well point to the accumulated systemic advantages of Qin (especially after it had already destroyed Han and most of Zhao) and say that Chinese unification under said state was inevitable.
As for its impact on China - a Qin unification of China will mean a legalist totalitarian state, no doubt - but it's important to remember that most other states were pretty much heading in that direction anyway, due to the systems needed to a) mobilize large forces to send onto the battlefield and b) 'proof' the ruling classes from being infiltrated by spies from neighboring states. I think Qin Shi Huang's megalomaniacal tendency is responsible for the massive centralization of China under his reign, but his legacy in that field was short-lived anyway as the early Han certainly did not copy his example. One could argue that if a non-Qin state unified China this would mean that the center of power shifts eastward, which would place the economic/political heart of China in areas more suitable for riverine/oceanic navigation and with less need for massive hydraulic/public works projects - that by itself would change China's destiny by some way.