Does Quick Claw negate lower priority?

Question

I recently read here a moveset for Dragalge, which recommended Quick Claw as held item and Dragon Tail as one of its moves. So, if Dragalge uses Dragon Tail and Quick Claw activates in the same turn, it's priority will be +1 or -6?

Answer 1

No. Moves like Dragon Tail will still have negative priority.

This is because Quick Claw can allow a move to strike before moves of the same priority bracket. It won’t, however, make a priority -6 move +1.

When this item is held, the user has a 18.75% (Gen 3 & 4), or 20% (Gen 5 & beyond) chance of attacking first if the moves all Pokémon use are within the same Speed Priority level.

Source

Proof

Comments

So if it says on "the same speed priority level", if all pokemon on the field used a -6 priority move, would the dragalge move first?

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Yes, under those circumstances, Dragalge should move first if Quick Claw activates.