Q. Does this also mean I should not even enter myself as a student in Turbo Tax?
A. No. Being a student can affect other tax attributes.
Q. I received a 1098-T but my employer pays the school directly. Is it correct that I don't need to enter the amount in Box 1 of the 1098-T ?
A. Yes, probably.
First, the 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for an education credit or possibly the student has taxable scholarship income.
If your employer paid all your qualified expenses (tuition, fees, books and required computer) with tax free money, you can not claim a education credit.
But employers are only allowed to give you up to $5250 tax free. If they paid more, the excess was most likely added to your W-2 as imputed income. You can claim a credit based on the excess (your after tax money).