From the pure math side, there is no limit to how many times you can accumulate gradients.

\frac{\partial \mathcal L}{\partial \theta} = \sum_{accumulation} \sum_{batch\_size} \frac{\partial \mathcal L}{\partial θ}(x_i, y_i) = \sum_{larger\_batch\_size} \frac{\partial \mathcal L}{\partial θ}(x_i, y_i) 

I guess, there would be more numerical accuracy / stability issues. Maybe the results would be a bit different from the “true” batch_size=256, but not too much.
I don’t think you need to adjust the learning rate, use the same value you would use for batch_size = 256.
Also remember that it is deep learning — even if you are sure everything is going to be alright, it may be quite different in practice. Just try it out and see.