No.
For a start you're missing the nature of the mutiny. It was a Muslim uprising against the infidel, with some (minor) backing from some high-caste Hindus. They were not really an organised army in that sense.
Then you have to deal with the fact that the majority of the Indian Army remained loyal. The proto-Taliban mutineers are a few thousand headless chickens running around, whereas there is a loyal force of ca. 150,000 Indians and 100,000 Europeans ready to crush them.
You're
really mischaracterizing the Mutiny. It wasn't at all just a "proto-Taliban" mutiny, it was much more lateral across Indian society at the time. However, that was certainly a character of some of the mutineers (I would argue though some of the upper-caste Hindus were much, much worse).
Most of the mutiny was disenfranchised landlords (taluqdars) who'd lost land under the Lapse Doctrine and their peasants. The old aristocracy butted heads with the British EIC and they were losing. Rani of Jhansi, who's since been lionized in Indian lore was actually completely willing to compromise with the EIC if they recognized her son as the rightful ruler of Jhansi. It also helped the mutiny that even amongst their allies, the EIC was pretty much well mistrusted because of their wanton expansionism and well, greed. Not that no other Indian had ever been greedy, but a lot of lives were disrupted by EIC trade and public policy (as good some of it would be later for the foundation of India).
There were religious issues too obviously. Some brahmins felt that the British reforms (abolition of sati, divorce, etc.) as well as increasing missionary work was "eroding their civilization" and corrupting the moral character of Indians, etc. (i.e. they liked the caste system where they were on top). As side note, it was actually most radical Hindu sects that opposed women's suffrage and education etc. For some Muslims, they felt the Mughal Emperor was disrespected when he left the Red Fort, the using of pork grease was a violation of their religious edicts, British had no respect for their traditions etc. However, there was no overwhelming wave of jihad that spread amongst muslims. There definitely were calls to jihad and the defense of the faith, but most of these were people were just on the fringe. For instance, Aga Khan, who had many more times the support of Khairabadi, supported the British (who formally recognized his title after). There were plenty of Indian Sunni muslims who didn't want to support the rebellion because some of its main proponents were Shi'ite, etc.
A lot of the EIC's most favored kingdoms/sultanates were muslim (*cough* Hyderabad *cough*) and because muslims in India at the time were mostly urban the British were exposed to them much more often (and so more of them worked alongside them, etc.)
With that out of the way, it's hard to get this specific rebellion to succeed. Basically the Mutiny was doomed from the start because it was more a gradual eruption of disenfranchised former-elites fighting out against the new elites, coupled with some religious factions and a few people still squabbling over hundred-year old wars. What I mean to say is: it was
very disunited.
For the actual 1857 Rebellion to turn out well you'll probably have to have mass destruction of railroads and transportation but more importantly you'll need more unified forces for the rebels. It really depends on how far you want to go back. If you can somehow get the Sikhs and Pathans to
not support the British, it would deal a significant blow to them in the north (as both played a pretty big role in recapturing Delhi). More former-Maratha states supporting the rebellion as well as more cohesive support from Islam would be needed as well. Had the Indians had a commander and some sense of unity the British would've crumbled, as they simply didn't have the manpower to fight off that kind of force. But unfortunately, India was by no means unified at the time and certainly not enough to military stave off the British. You can do a lot more damage to British infrastructure this kind of rebellion though, and it would likely lead to more slaughter and violence on their part (they basically pulled a Nanking 90-some years before people really cared). That would definitely affect any future independence movements and might lead to more open rejection of British rule in some fringe areas of the Raj.