A basic question about opamp buffer offset and input offset voltage
The input offset voltage would be multiplied by the gain in the circuit you show. There is no feedback at all (ideally). In a model of an op-amp with gain A , infinite CMRR and offset voltage Vos, the output would be Vout = A*Vos. A is usually quite large, so the op-amp output will be railed to one side or the other, depending on the sign of the offset voltage.

If you model common mode rejection there's another term that changes the output voltage from the common mode voltage, but that gain could be positive or negative and even if it happens to be negative, it may not be able to balance out the input offset voltage before the output hits the rails, so the output is unpredictable, but likely railed just as above.