Sadly, no. He seems to be fine for boss mechanics specifically, but... I'm taking a look through your baleroc kill, as that's closest for the ideal arcane fight. As mentioned above, crit is pretty poor for arcane. He should be pulling stats out of crit into others, not out of haste into others.
Baleroc. I see no evocations, period; the spec is a burn and evocate into conserve mode until the CDs come back up. He appears to be using mana shield either after the damage is done or when he won't be taking any, which are wastes of GCDs; all but one of them was a complete waste. This was a 5:49 kill, and wasn't using evocate, but only managed 3 arcane power and 2 presence of minds. These are 1:30 cooldowns. Given he's not using evocation for some reason, he should have been using them on CD. Looking at damage specifically, he only cast flame orb once, when he could have gotten 6.
Your entire raid night, he evocated 4 times total.
Please direct him to the sticky at the top of the board on how to play arcane. He clearly doesn't understand the mechanics of the spec, by any stretch of the imagination. The dude's got 6 item levels on me, and VPLC which is a ~1k DPS proc, and I'm beating him silly in terms of damage, as frost. He might be great for boss mechanics, but to be honest, he's a shitty mage. I hope you can convince him to do some homework on the class and get him up to par.
Edit: Throwing the AB debuff graph up with the other picture. I really wish this had a mana graph sometimes, this would be fascinating to tear apart.