https://www.mshistorynow.mdah.ms.gov/issue/cotton-and-the-civil-war Well, yes. You CAN get by without cotton, and that is largely what the North did, even destroying a lot of cotton grown in the South as a war tactic. Obviously the North won, largely because her industrial and diverse economy outdid the South's agrarian one.
The cotton industry was one of the world’s largest industries, and most of the world supply of cotton came from the American South.
[ . . . ]To begin King Cotton diplomacy, some 2.5 million bales of cotton were burned in the South to create a cotton shortage. Indeed, the number of southern cotton bales exported to Europe dropped from 3 million bales in 1860 to mere thousands.
[. . .] But when the cotton famine did come, it quickly transformed the global economy. The price of cotton soared from 10 cents a pound in 1860 to $1.89 a pound in 1863-1864.
The South stupidly thought by refusing to sell its cotton, it would bring European nations to its side. This was before the blockade became effective. Had they sold cotton then, they would have had more money to fight the war.
If you look at what was available to both sides, the South had little chance of winning even though their conditions for victory were much less than the north’s—the north had to conquer the south, while the south only had to avoid being conquered.