Yes, the income has already been factored into your wages which is why you have a cost basis. You will not see the breakdown for Box 1 per se, however your W2 does provide information in Box 14, your pay stubs may also show a breakdown or the statement is used to provide it without an additional entry on the pay stubs.
Adding the award to your wages eliminate double taxation because you have a cost basis to use against the sales price. The only income on the return from the sale will be the appreciated value on the date of sale.. You should calculate the basis at the time of the award based on the fair market value on that day (which is also the amount included in your wages and, if applicable, any amount you paid at the time. In this situation you may not have paid anything on the date of the award which is also common.
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