Would it? Most new smelting plants today in the US (any built in the last few decades) use a mixture of hydrogen and carbon monoxide as the reducing gases (natural gas primarily as feedstock, but no reason it couldn’t be about 90% hydrogen produced via, say, hydroelectricity or wind).
Coal didn’t overtake charcoal for smelting iron in the US until the latter half of the 19th century, well after the first industrial revolution.
Melting down scrap iron is one of the main sources of steel in the US, and that is done straight with electricity in arc furnaces.
Coal accelerated the second industrial Revolution, but it was not essential. Far more important for enabling the first industrial Revolution was some of the early scientific knowledge about steam and pressure, such as the work of Robert Boyle, a lot of that based on a sort of reaction to the classics that had been revived in the Renaissance. The biggest argument for coal is indirectly in that it helped the viability of British society (after the island had most its tree cut down over the previous 500 years) which played an important role in the Scientific Revolution (Robert Boyle was Anglo-Irish)… although by the time Britain was playing an important role, the scientific Revolution was already underway on the mainland of Europe. As long as our books are not all destroyed, I think we’d have no problem bootstrapping from charcoal the second time around.
(I think a lot about long term data storage… writing in stone or fired clay still seems like one of the best methods for writing that needs to last 10,000 years… it was, after all, preserved Greco-Roman classics that enabled the renaissance and therefore the scientific Revolution.)
I think that vastly underestimates the dependency tree in modern society. Storing hydrogen in useful quantities is tough, requiring fairly sophisticated metallurgy and cryogenics.
Finding out we've got a hard to replace left-pad module somewhere far up the tech tree wouldn't be fun.
The dependency tree of 19th Century or early 20th century society is a lot more straightforward, however.
And no, you don't need such sophistication for storing useful amounts of hydrogen. Storing large amounts of hydrogen (in this case, also mixed with poisonous CO) was solved in the beginning of the 19th Century (well, late 18th century) in Britain and Germany by using very large near-atmospheric storage vessels called Gas Holders: https://en.wikipedia.org/wiki/Gas_holder
Yeah, I think we switched to coke during the Industrial Revolution not because it's a better fuel than charcoal, but because we were running out of trees.
Coke was Abraham Darby's doing (around 1709-1710), and that was mostly to corner the market for cheap pots and kettles. There was no way for the charcoal crowd to compete on iron, and the bronze bunch - the norm for that sort of thing up to that point - was left forever in the dust.