[ig06]

In this specific example (with the assumption you state that bb pushes any turn) I think it is better to call the flop and re-evaluate. I make the assumption that you also call the turn if you hit a T or 9 (which is clearly correct against the AA you give in the example). Here is my calculation. I neglected to consider rake but it makes no difference here.
Case 1: Push.
You invest 890 into the pot.
Final pot size is 2005.
Your equity: 52.626% (pokerstove), i.e. 1055.1513

1055.1513-890 = 165.1513
So getting it all-in has EV +165.1513

Case 2: Call 200.
On turn: Pot 625, stacks 690. Pot equity needed to call on the turn push : 34.41%

Any 7 or Q and he is drawing dead. Any of the other 6 hearts (excluding 7,8,9,T,J,Q,A) and he will be drawing to 5 outs with 44 cards left in the deck.

So 8/45 times you get 100% equity on the turn.
6/45 times you get (39/44)*100% equity on the turn =88.636363…%

A T or 9 gives you any 7,9,T,Q or any of the 6 unaccounted for hearts as outs, which means you have 18 outs (two 9s, two Ts, four 7s, four Qs, six hearts.) so enough to call.

So 6/45 times you get (18/44)*100% equity on the turn =40.90909…%

25/45 times you have to fold the turn.

So your EV is (25/45)*(-200) + (20/45)*(-890) + [(8/45)+(6/45)*(39/44)+(6/45)*(18/44)]*2005

= -111.1111-395.5555+702.7626 =196.096

i.e. 25/45 times you lose 200 and fold the turn (first term).
20/45 times you invest 890 into the pot (second term).
8 of those 45 times you get 100% equity in the pot, 6/45 you get 39/44 equity and 6/45 you get 18/44 equity (the bracketed terms).
So calling and calling the turn push if you improve has an EV of +196.096 which is better than pushing the turn.

However, do you think you ever have this scenario? I mean this assumes that villain always pays you off when your draw gets there and that his range is limited to exclude sets, bigger flush draws, hands that fold the flop, etc. I don't think it needs much of the latter (i.e. fold equity) to make pushing better (especially if he sometimes folds when you call flop and hit your draw). Also, I think people like pushing big draws to balance with sets, etc.