Looking at the numbers you posted, I think a decent estimate of what you're looking at is this...
Before
48K hp
55% Avoidance
After
40K hp
65% Avoidance
By adding that 10% Avoidance, you will be reducing overall incoming damage by 10/45 = roughly 22.2%. You will reduce the chance of getting hit twice in a row from roughly 20.3% to 12.3%. And reducing the chance of getting hit 3 times in a row from 9.1% to 4.3%.
Problem is, as posted above, will you have enough hp to survive the worst case scenario? Say the boss is hitting you for 20K+. If you get hit 2 times in a row, which WILL happen 12.3% of the time, which means many times in a boss fight, if you're healing is slow for whatever reason, you'll die. If you get hit 3 times in a row for 13.3K+ each, which WILL happen 4.3% of the time, probably several times in a boss fight, if your healing is slow for whatever reason, you'll die.
So I think it would work fine most of the time. If your healers are quick reacting, you'll be fine, even when your avoidance doesn't work and you get the strings anyway.
But from time to time (maybe 1 in 10 boss fights as a wild guess), the stars are going to align, 2-3 big hits in a row are going to land anyway, and healing is going to be late for whatever reason, and you're not going to have the hp to survive it, and "squish". The raid is going to wipe, and everyone's going to be like wtf? And you'll *grin* sheepishly as everyone runs back from the graveyard and say, sorry, had an unlucky streak of hits there, and my healers weren't quick on the ball, and I died. Better luck next time?
Then again, every now and then, maybe one of your healers dies down the stretch... maybe all your healers are running out of shadow crash on Vezax at once, and all healing stops for 3-4 seconds. But you hit an avoidance streak that you otherwise wouldn't have hit with your lower avoidance previously.... you live through it and down the boss. Your avoidance saved the day. /cheer So you could get lucky in a good way every now and then, too.
You also have to consider that if you are a warrior tank, 22% less incoming damage means 22% less rage from incoming damage. It is going to have a severe impact on your threat output. And an "unlucky" avoidance streak at the start of the fight could wipe the raid if the boss is untauntable (like Vezax). This won't be an issue come 3.2, because you can get 5/5 Shield Specialization. But it will be now.