No. Each job is completely separate. Actually a W9 is for self employment income. You will be getting a 1099Misc from the side job. Not a W2. They will not take any taxes out of the side job so you might want to pay in an estimated payment to cover the income tax on it AND to cover the additional self employment tax on it. Instead of paying in a separate estimated payment you could increase your withholding at your full time job to cover the extra taxes. Even then the full time job won't know anything about the side job.
