From what I remember of Stephen Platt's book about the Taiping (it's organized as a sort of narrative collection, a series of interlocking biographies about major figures on all sides of the war) his reading seems to be that Zeng was depressed and pretty much wanted to give up his job as soon as possible; not to mention he was old and had health problems that made him even more miserable. And despite being an excellent logistician/organizer (what let him build an army from nothing and with no personal experience in the first place) as a tactician he was outshone by his contemporaries, including his brother Guoquan.
He's really not the right person to found a new dynasty, but if somehow he did do it... well, a lot of the people he elevated (Li, Zuo) ended up in power within the Qing structure OTL anyways, and they still failed-- and not just due to Manchu obstructionism either. The Xiang and later the Huai Armies were not perfect structures. The model of recruitment Zeng used for the Xiang (and later taught Li to use for the Huai) was recruiting through webs of connections, sweeping up particular age-cohorts from villages and organizing them as a unit, then a cluster of nearby villages as a larger unit, such that each person was fighting along people who they knew/felt some obligation to (and who would know where to find them if they deserted). It was effective for putting together a cohesive, motivated force against the Taiping (especially when on the defensive). But in the longer term... "Xiang" is an abbreviation for Hunan, and "Huai" for Anhui, they're fundamentally built around provincial loyalty and personal approval for the commanders rather than any ideology. The connection between this and the later warlordism is not particularly cut-and-dry, but there was a lot of factionalist "us vs. them" sentiment among leading figures and their powerbases that led to absurdities like China splitting its resources among four different fleets in the lead-up to the Sino-Japanese War and then soundly losing the naval theater of that war.
A hypothetical new dynasty would already be starting off on the wrong foot due to an unenthusiastic and ailing leader, and from there the built-in tendencies toward factionalism and private-armies-in-all-but-name will assert themselves. End result: Yuan Shikai probably enjoys a very similar career as OTL, w/ similar results