If you're inside that ring when the Arcane explosions go off, you're pretty much always dead.
It does more harm than good and will often end up instantly killing you, but I can confirm from memory that this wasn't always the case. It seems the spell casting system was revised so that spell combination has that unfortunate side effect. Maybe intentionally, it was pretty overpowered. In the video, you can clearly see that the Arcane explosion from the spikes does no damage to the player, which is no longer the case.
Some workarounds you could try:
Use it to enchant your weapon, then do a swipe with it. This casts the spikes in a straight line away from you, so you'll take less damage, or none at all if you run away from it.
Cast it normally and backtrack to avoid the explosion damage.
Cast it as an area effect, then quickly teleport out of the ring using the Teleport Magick (ASA).
Try casting it without Arcane, which makes it not explode (i.e., safe to stand in), but also, of course, weaker. You can add additional Lightnings to make it last longer.
As for your original question: It is actually possible to survive the full blast, but not reliably. If you use the Epic Robe, which has Arcane resistance and increased HP (Gamer BundleGamer Bundle DLC), have full health, cast a self shield at the right time and keep boosting that as the explosions go off, you can emerge from the ordeal, but very much scathed.