Antennas --especially big ones-- have a large radar cross section, i.e., very visible on the radar. So a stealthy ship wants to avoid them. At the same time, long distance communication requires very large wavelengths and therefore large antennas. Temporary antennas are a good solution.
EDIT: this is of course in the article. Note to self: RTFM
The fountain part of the video didn't make sense to me. I suspect the salt that would be added to the water in the fountain would have a corrosive effect on it.
He says in the article that you need 70-80ft for HF, 6 ft for VHF and 2 ft for UHF, so I would guess so.
However they do also say you can use plastic tubing with it, so I guess carrying around 6ft wouldn't be hard, though how practical that would be in rough conditions is questionable.
Magnetic anomaly detectors are already used by many navies for submarine hunting and minesweeping.Typically mounted on aircraft. They use to use similar equipment in the Vietnam war to detect truck ignition coils.
So quite possibly the magnetic field could be detected. On the other hand,if you're transmitting radio, then you can be detected. And if you had an normal antenna, that also sticks out like a sore thumb on radar. It took a LOT of work to get the radars on the stealth fighters not to light up like a Christmas tree. If you could set up your transmission to be fast enough (burst transmission), then your magnetic field would be up for too short of a time to be useful (possibly), much faster than a mechanical antenna can extend and then retract.
Basically, I'm sure they thought of that. War is their business, they tend to be pretty good at it.
But the ability to 'dismantle' the antenna for stealth makes sense, as well as the ability to change the size of it on command.