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Not quite. Weapon speed factors only matter with determining which strikes occur first in simultaneous combat, or in a spell-vs-weapon situation (DMG pp. 66-67).
In this particular case, the skeletons, winning initiative, manage a swing against the PCs before the attacks and Turn Undead occur. Turn Undead does not have a spell casting time nor a speed factor (and cannot be spoiled by a successful attack), and can resolve first--or even before or after Amirad's strike, as his choice.
So, we've got the following:
Austin turns the skeletons.
Amirad charges a skeleton.
Lidia draws her cudgel and prepares to attack any skeleton that approaches.
Sarge prepares his shield and weapon to defend Lidia and Austin.
The skeletons close and attack.
Now, for initiative: The skeletons get a 3, the heroes get a 2. The skeletons strike first--with the exception of Amirad, who charges (DMG p. 66); weapon length is what matters. Amirad's sword had a longer reach than the skeletons' attacks, so he acts first, with +2 to hit.
The order for strikes is Amirad, the skeletons, then Austin's Turn takes effect.
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Amirad rushes in against the skeletons, but has trouble keeping his footing on the uneven ground, foiling his swings.
The skeletons lash out at Amirad, Sarge, Austin, and Maruial. The one attacking Austin manages to strike him with the pick just before he unleashes his holy power, and the skeletons turn and run down the passage, away from the party!