How much do you think she heals off Q?
Like, let's put this into perspective, shall we?
Akali needs almost max energy to heal off Q. Let's say she's going into some ranged mage, right? Q heals for 40% of the damage dealt when you have enough energy. The move does 125 base + .65 AD + .5 AP. The most AP you're going to have from items, while building Gunblade first, is 40, so +20, and the AD you'd have at level 9 would be about 110 (base AD + Cutlass), so +71. This means your Q does about 200 damage at rank 5, assuming she just has the parts for Gunblade without the entire thing at level 9. You heal 40% of this in one high energy Q.
...that's like 80 healing. At rank 5.
Literally ANYTHING can negate that healing. Sure, you get ap from runes, but you're not going to get enough to significantly alter the numbers. She can easily be poked down through this amount of sustain unless she goes for minutes on end without receiving further damage.