The liquid has to be insulator (doesn't conduct electricity) and so if you can sink the miner in it, there is no reason why you can't include the PSU, the only problem I can think of is that PSU might not work if the fan isn't spinning, so I don't know how they go about solving this issue, but I think since you are trying to cool the miner, there is no need to bring in the PSU's heat along, just put it outside the cooling box/container.
You are also going to face the same issue with the miner's fans, but most custom firmware allow you to run the miner without fans, if you chose to run the stock firmware you will need a
fan simulator, it basically tricks the control board into thinking that there are two fans spinning at 5000-6000rpms and so the stock firmware will work just fine.
... can I just dip it in liquid and it still work as if it's in the air?
Yes.
