Are the Offset Voltages in a Dual/Quad Op Amp Correlated?
No.

The offset voltage comes from the difference between the two input transistors in the same opamp.

The input transistors in this TL072 are interleaved so that they have the same center, so that if the transistor parameters are varying linearly across the die, the average parameters are the same. Despite this the transistors are still slightly different because the variation is not exactly linear.

So if the two transistors right next to each other are mismatched, why would the ones on the other half of the die have the same mismatch?