I feel like the instructions somewhere explicitly say not to do that, but I can't find it now. Either way, I would highly recommend not doing that.
The water doesn't go directly from tank to pot, it goes down, over, and up, through the entire machine, so when you're done, there's going to be residual water throughout the machine. If this were milk, it would all spoil and gunk everything up, so at the very least you'd have to run a cleaning cycle or two immediately after every time you make hot chocolate this way.
I'd pick a much cheaper, easier to clean device, like an electric kettle. I don't know if these are designed for milk specifically, but if you were going to try it, these would be much easier to clean afterward.
Brentwood - 1.7L Electric Kettle - Red
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Kalorik - Electric Kettle - Stainless steel