No, it doesn't.
Arguably, the structure of US income (including payroll) taxation discourages labor and, even moreso, employment, but that's not inherent, but a result of deliberate inequities in how different sources of income are treated.
If instead of paying somebody $20/hour you need to pay them $30 because of taxes, that makes hiring them more costly and you're incentivized to look for other options.
Now, the specifics of the US system of taxation on income discourages labor/employment quite heavily, by tax favoring income through gifts and inheritances (up to a very large quantity) over capital income, which itself is favored over general income, which itself is favored over labor income. But none of that is inherent in the concept of an income tax system.
That's seems true regardless of other taxes. The only way it wouldn't be true is if raising taxes on labor also raised taxes on all other possible actions in somehow an exactly symmetrical way.
If the government has to raise $N total in taxes, that amount of money is coming out no matter what. It has to come out somewhere. The real question is distribution, and that's when you have to look at fairness of taxation and ability to pay. You can't just say income taxes discourage labor and ignore the question of where you're getting the taxes instead, and how the alternative taxation method affects labor.