Danger Sense does not replace the required save with Dexterity because it can be seen - and specifically it does not activate in the case of Shatter.
Danger Sense gives you (PHB, 48)
Advantage on Dexterity Saving Throws against effects that you can see
Shatter is a Constitution Save and therefore Danger Sense doesn't apply. Danger Sense does NOT change the spell/effect's saving throw, it only gives you advantage IF it is a Dex save.
A specific example of where this would work is Fireball - which is a Dexterity Saving Throw.
Thematic Equivalence
The current third level ability Warrior of the Gods states that your soul is marked for endless battle. The functional aspect of this is that when you die and someone casts a Resurrection type spell there is no material cost for the casting. This allows the zealot to more easily return to keep fighting for their God(s).
In a world without resurrection, what can give this flavor without making the Zealot overpowered?
My idea riffs off Yakk's, but introduces some additional consequences. While I really liked the idea presented, I think that it is much more powerful than the original.
The original still requires a caster and for them to expend at least a 3rd level spell slot - if not higher. Additionally, unless Revivify (PHB, 272) is cast, there will be a fairly steep mechanical penalty for the resurrection. Namely:
The target takes a -4 penalty to all attack rolls, saving throws, and ability checks. Every time the target finishes a long rest, the penalty is reduced by 1 until it disappears.
In order to balance the Zealot's 3rd level ability in a world without resurrection, similar penalties need to be incurred. The following is my suggestion:
Warrior of the Gods
At 3rd level, your soul is marked for endless battle. When you take damage that reduced you to 0 HP or suffer and effect that would cause you to die while raging, you may instead use a Rage to return to life with 1 HP and gain temporary HP equal to 1/2 your maximum HP value that lasts for 1 minute. You will also be exhaustion level (4). Once you do this, you may not use this again until you have completed a long rest.
Exhaustion Level 4 (PHB, 291) has the following effects:
- Disadvantage on ability checks
- Speed Halved
- Disadvantage on attack rolls and saving throws
- Hit point maximum Halved
The balance explained
In the original ability, it was required to find or have a caster who had the necessary spell slot available. When coming back (except for Revivify), the penalties are also very big. Allowing the Barbarian to bring themselves back is a big boost, as it becomes an on-demand ability. In order to mitigate this, I have set up a once per long rest mechanic. This way, the Zealot is immediately back up, but with many of the penalties typically given to a creature who has been resurrected.
Best Answer
As long as the effect is projected from the invisible caster, yes
Greater invisibility states:
When you are casting a spell that projects an effect (like fireball or lightning bolt) you are not wearing or carrying the effect and that effect is certainly not on the caster's person. This means that the effect becomes visible as the caster casts it. And since you can now see the effect, danger sense applies.
However, if the effect is not projected from the caster, and the DM rules that the effect fulfills the requirement above, then danger sense wouldn't apply since the magical effect itself would be invisible. I have never seen a spell combine with greater invisibility in that manner though.