Yes. The test mod runs at 8.2v with fresh bats (2x14500 in series). This one uses an 801 atomizer so I set it between 5.0 and 5.5 for my usual vaping. I used an LM317 for the regulation in this one, unaware of the drop off issues so I don't have the full voltage range that I wanted on this one.
I now have smaller higher quality pots and some UC283-ADJ LDO chips so I should be able to get a complete range of voltages with less drop off than you get from a 1N4001 diode.
Edit: I just read your question closer and I'm not quite sure I understood it. The current fluctuates (sags) under load like all batteries do at source. The current is obviously shaped during regulation since the resistance of the atomizer is a constant.
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