I doubt that, given how Rune Axes work and that Rune Chopper shows the same MP pattern. If your MP is 0 at the start of a tick, you don't get the latent that tick.
I've used it a lot myself. Once your initial MP pool is drained, you alternate one tick going from 1->0 MP and +5 HP, then next tick 0->1 MP and no Regen. If auto-refresh were applied first you would get +5 HP every tick and stay at 0 MP, which doesn't happen.
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