We don't have to idly speculate this, the phenomenon is called elasticity of demand in economics, and not only are there good estimates of elasticity for various products, there's a rich set of ideas that have been developed around elasticity, including what happens when you tax goods of various elasticities.

I highly recommend looking into the details yourself (any intro micro economics textbook will cover it), but the upshot is that cigarettes judged to have relatively inelastic demand, which is basically what you had said. This means that a tax on the product will not reduce the equilibrium quantity consumed by very much. A corollary is that the majority of the tax burden will fall on the consumers of cigarettes. I'm not sure why you said "most of the money goes to the tobacco companies"-- with all tax levels the revenue goes to the government.