I don't like raising AJs very much, but because it is suited and your position is OK it isn't a big mistake.
The reason why I don't like it is very simple, you will have a real problem to lay down your hand on the board A47, but a good opponent won't raise you preflop with AQ or AK.
As you said, you have a lot of outs.
9 flush
3 straight
2 trips
3 aces
Lets discount 3 and you are left with 14 outs, there is no way you can fold this in a pot this size, even when we would see a turn, the pot is huge and we can't fold anymore. So when there is no way to fold the hand anyway, we try to get the money in as long as we are favourite to win this hand and we have to push over the raise in front of us. This has an other positive effect, when we hit the nuts, villain has all its money in the pot and can't decide to fold.