Has a 100% chance to proc on Icy Touch, gives 53 def rating (which is closer to 11 def skill, not 3) and should be up 100% of the time given that it lasts 30 seconds and Icy Touch only costs 1 frost rune. Even discounting death runes, you would get 3 chances to refresh the buff before it dropped, presuming that you spammed a frost ability every time it was available.
I would consider this to be in the same league as a Paladin's Holy Shield. For all intents and purposes, when calculating overall avoidance + block for a paladin, you add 30% because Holy Shield has a shorter cooldown that the duration of the buff it provides. If your tank isn't vigilant about refreshing it, they're going to get into trouble, but there is no reason they shouldn't have it up 100% of the time (save for situations where the charges are consumed in less than 8 seconds, but those are few and far between, and in any case there is no similar consumption of the DK sigil's buff)
The sigil grants a buff that more than covers the minor, minor gap in defense from his gear, with a 100% procrate. For all intents and purposes, he's crit immune with the sigil, assuming he refreshes the buff. It was introduced a few patches back with the intent of giving deathknights another means of reaching that crit immunity, due to the lack of any tanking 2handers to speak of.
If his defense is that low, he's probably using a swordshattering runeforge, which is a very viable alternative to ssg.
Whether he's geared enough to MT Naxx..... can't really say without an armory profile to look over. But from what you've said, it's quite possible that he's geared just fine to tank the zone.
I'm going to say if he has the HP pool and the general gear then yes he is ready. He is Def. capped during all fights. Unless he is bad, I used that sigil and had about the same Def at some point too because it allowed me to get a little more stam which I badly needed when less geared.