Vigilant Strike + Disciple of the Unyielding?

Can you now bypass Vigilant Strike's cooldown with this passive? It gives you a +1 minimum endurance charge which (not grabbed it yet to see) tells me you have an endurance charge on you at all times.

No, you can't.

https://pathofexile.gamepedia.com/Charge

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Minimum charges

Certain mods grant +X to Minimum Endurance/Frenzy/Power Charges, causing your character to always have that amount of charges.

Skills and effects that consume charges to activate an effect cannot use these minimum charges. For example, using Flicker Strike with +1 to Minimum Frenzy Charges at 1 Frenzy charge will never use that charge to remove its cooldown.

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CPTBRUMBL3Z wrote:

Can you now bypass Vigilant Strike's cooldown with this passive? It gives you a +1 minimum endurance charge which (not grabbed it yet to see) tells me you have an endurance charge on you at all times.

No, as the poster below your OP explains.
It's a bit messy, IMO. But when you think about it, it makes sense. You will always have [minimum] number of xcharges. So when a skill would remove a charge, it couldn't, since [minimum] would then be [minimum-1], which it can't be. So from the POV of the skill, [minimum] is the new zero. From the POV of effects on you, the charge is still there, granting crit chance, defenses or damage, based on which charge it is.
The wording for what you're looking for would be something like: Instantly creates [number] xcharges when you reach your minimum number of charges.