An AAA NiMH delivers a max of 800 mAH (irrespective of what it says on the label). So 600 mAH would be 3/4 times as big. 7 of those would be close to 9V. 3/4 of 7 is 5.25. So, is it possible to fit 5.25 AAA cells in a 9V space? I doubt it, especially considering that the 9V battery has an additional layer of packaging. I'd say, at most 500 mAH may be the absolute max possible, if one tries really hard. 300 mAH - 400 mAH is more realistic, especially if you want the low self discharge type.
As per comments below, an AAAA cell could potentially be 480 mAH max. 6 such alkaline cells typically make up an alkaline 9V. So for an NiMH 9V, if you have more than 6 cells in the same space, the mAH will almost definitely be less than 480 mAH.
AAAA NiMH exist, and are 400 mAH. However, you need 7 of them for 8.4V (nominal). Or, you can make a 7.2V 400mA battery with 6x AAAA, that looks like a 9V battery (PP3 battery).
6x NiMH will typically be at 8V for most of it's life, at <100mA current draw. I use this often (6x AA NiMH). This is not as bad as it sounds. Remember that most manufacturers rate the alkaline cell mAH down to 0.9V. That means 5.3V for an alkaline PP3. 8V is way better than that.
Also, somewhat unrelated, but... Rechargeable cells are best charged singly. In a battery, if any cell is more damaged than the other, there exists a chance of polarity reversal during charging, which will destroy the pack. The chance of this happening, increases with every additional cell in the pack.