Not really. Horford is paid like a superstar, yet he clearly isn't one. He's a very good player, but no one will make the case he's all-NBA. If he played for GSW, he'd be their 5th best player, and very few would dispute that.
He made the All-NBA 3rd team in '11, and he's a four-time All Star. The thread's question is whether IT/GH/AH is a big 3, not the biggest big 3.
That was 6 years ago. The question is whether or not it's a big 3 now, not if it might have been in 2011. A 4 time all star in his 10th year is evidence he's a good player, as I said he was.
But, he's a borderline all-star now. He didn't even make it in the perilously weak east last year. To me, a borderline all star isn't really part of any "big 3". Pierce and Garnett were 2 of the 10 or so best players in the league in 2007, and Ray Allen was a perennial all star. That's a "big 3". That's not to say Horford can't be a big part of our next title, but the reality is that if we win a title in the next 3 years, it will be far more likely that Brown or Tatum or someone else stepped up as part of a big 3, rather than Al Horford.
I like Horford and I don't wish that Ainge hadn't signed him, but it's hard to make the case he's even among the league's best 25 players. IMO, there's really no way to include him in a "big" anything.