We don't compute per-example gradients, so in your second code snippet there would not be a loop across examples. We compute the batch-averaged gradient in the same time it would take to compute a single example's gradient, so it's much more efficient than your proposal, which is equivalent to using a batch size of 1.
You're right what you propose is not quite equivalent to batch size 1, as you don't update the parameters until processing the entire batch.
Still, having to process the examples in a batch sequentially seems like a very costly concession to make. Traditionally the reason to use batches has been because GPU-style parallelism makes them cheap. If you take away that reason by making the computation sequential, large batches become much harder to justify. Moreover it's not clear what you gain by making the computation sequential in this way -- do you think Adam actually has trouble keeping up with mean/variance of gradients so it needs more frequent updates? I would be surprised if so.
