I don't believe PADI has much of anything to do with SNUBA.  I would expect
that, if they did, you'd have to be certified to use it.

No, SNUBA is not safe, at least without a bit more training than you suggest
was happening.  One of the most significant risks divers learn to avoid is a
lung overexpansion injury.  When they occur, they are often fatal.  With
SNUBA, as with SCUBA, you are breathing pressurized gas at depth.  As you
ascend the ambient pressure decreases and any gas in your lungs expands.
The volume occupied by the gas doubles between 33 feet and the surface.  If
you have a lung full of air at 33 feet and you hold your breath to the
surface, there's a chance that you won't reach the surface alive and a
significant chance that, if you do, you will be severely injured.

Another problem with SNUBA is that you don't have a clue about how much gas
you have available.  People often have very different consumption rates.
With the gas, and the pressure guage, on the surface, and four people
sucking on the same supply, it's almost impossible to guess when the tank
will run out.  A trained, experienced diver would not think twice about
making it safely to the surface from 20 feet.  I wouldn't want to bet on 4
untrained, inexperienced divers all doing the same.

Lee

Here's a cut & paste of how I answered a previous question about snuba.

"Snuba" is a trademark for a company that markets a particular variation on surface
supplied air. They also have a patent, which is probably a good example of a patent
that should never have been issued, due to prior art and their particular application
being obvious. The tank floats in a small raft (that's what the patent is about), and
it's usually done from the beach. You don't need a compressor or a boat. Snuba limits
you to 20 feet, because that's how long the hose is, but commercial divers using
surface supplied air go much deeper. You can also get small compressors that float on
the surface and usually have a 40' hose. Snuba claims to have an excellent safety
record, but from a physical or physiological perspective it's no different than
regular scuba diving in most respects. Because your depth is limited it's extremely
unlikely that you could get bent, but if you're at all careful with regular scuba
it's still very unlikely. What can still happen with Snuba are the more serious
injuries that result if you ascend without exhaling. Because of the pressure
difference between the surface and 20 feet down any air that comes out of the
regulator at 20 feet will expand about 65% on its way to the surface. If you exhale
at 20 feet the bubbles will get much bigger as they ascend. If you ascend without
exhaling the air will still do it's best to expand by 65% with your lungs offering
some resistance. If your lungs are much more than half full that will almost
certainly ruin your day, since the strength of your lungs is no match for the power
of the expanding air. When the air expands it can rupture your alveoli (the
individual air sacs in your lungs, if you didn't know), and/or enter your arteries as
an AGE, or arterial gas embolism. If you don't know what an embolism can do for you,
think blood clot in the brain and you'll be on the right track. In theory, it's
possible to damage your lungs by ascending as little as 4 feet, but it's not very
easy in the real world.

None of this should scare you, since all you have to do to avoid such unpleasantness
is exhale as you ascend, and those injuries are fairly uncommon. The first rule of
scuba is to never hold your breath. You should always be either inhaling or exhaling.
Of course if you jump in the water with no training and something causes you to
panic, bolting to the surface may seem like a good idea.

Now for some really good news. You can very easily go diving on your vacation without
becoming certified first, by taking a "resort course". Some here will tell you that
resort courses are terribly dangerous because the training is very abbreviated
compared to a real class, and others of us will tell you it's a good, and inexpensive
way to decide if you want to continue with a full course. For about $80 to $100
you'll have perhaps an hour of class time that explains things like expanding air,
and safety considerations, then you'll spend some time practicing basic skills such
as clearing water from your mask and recovering the regulator in case you spit it out
of your mouth. Once you're done with that you'll go on a dive that is supposed to be
limited to 40 feet for about half an hour. Compare that to Snuba, where the entire
process, including classroom, practice, fitting you with gear, and the actual dive,
lasts about an hour and probably isn't much cheaper (they've got similar costs to a
diving operator, plus paying fees to Snuba)