Such a tax would definitely affect people's use of energy. The reason for this is that it would increase the price of energy. If there were a tax on carbon emissions, every use of energy would cost more than it does now. The law of demand tells us that, all other things being equal, any increase in the price of a good or service will reduce the quantity of that product that consumers are willing and able to purchase. Therefore, a carbon emissions tax, which would raise taxes on energy use, would reduce the use of energy.
Unless the tax increases the price by a large amount, I don't think individuals will do much to change their habits. We've seen that as gas prices go up, people will trim their use of gas, but we have yet to see a mass exodus of people to public transportation (where available) or more people walking/biking as their primary mode of transportation.