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I'm the guy in the QB who will always pick up an AA gun or two if my opponent has a chance of having planes.  Got to wondering just how effective AA guns are at denying air attacks, so I ran a quick test: 1 US P39Q Aircobra (500lb bomb, 3 strafes) vs. 10 German HTs, spaced out in the open, far enough apart that a bomb could only hit one.  Ran 10 trials each of zero AA, 1 20mm AA, and 2 20mm AA guns on defense.

The results:
(bombs = avg. # of bombs dropped per trial, regardless of effectiveness, strafes = avg. number of strafes per trial, regardless of effectiveness, kills = knocked out HTs, shot down = avg number of planes shot down per trial)

AA guns    Bombs   Strafes   Kills    Shot Down
    0             1          2.3      2.4         0
    1             1          2.3      2.6         .2
    2            .9          1.4      1.4         .1

Again, maybe 10 trials each isn't enough to be statistically significant, but it seems like plane effectiveness drops way off when you have 2 AA guns, whereas one seems to have little effect (in fact, a slight negative effect, but that's gotta be a bit of an anomaly).

A few interesting side notes: During one trial with 1 AA gun, the plane actually showed up 5 times (a bomb and 4 strafes), one more than its 'maximum'.  Didn't know that could happen.  One trial with 2 guns, the plane didn't show up at all.  

I also didn't account for shocked/gun damaged results, just too much of a pain to keep track of.

Do with all that what you will...

Seems like AAA fire is pretty much hit or miss (pun intended) in CM. If you create an effective AAA umbrella you wouldn't have any points left for anything else. I think your tactic of having a few around is sound as it does apparently throw off aim.
During one glorious tournament bout I had a truck-mounted 37mm AAA take out ten vehicles... so AAA has it's uses. Thing to do is have them fire from key hole position or into flanks from hide.

I think the test instead shows that 20mm AA singles suck.

My experience is that a single 37mm, western Allied 40mm, or German 20mm Quad AA, is quite sufficient to deter most follow on strafing attacks. It easily cuts the effectiveness of enemy air in half, sometimes more. These types also have very high firepower against enemy infantry and guns, from 16 or so blast, high ROF, and very high accuracy. All but the 20mm Quad also have decent AP performance, enough to get damage results against full AFVs even if they can't penetrate, and to trash all lighter armor effortlessly.

The German 20mm Quad has the benefit that it is quite stealthy, compared to the larger calibers. It is also very cheap for the power at 32 points regular. The bigger types are better at damaging enemy armor, however.

Compared to these serious AA guns, I find the 20mm singles and the Russian 25mm singles, to be ineffective pop guns. Both for AA and for ground fire. They can suppress a single infantry target in the open and remain sound, but rarely hit more than 1-2 men even when they do that successfully, and their fire effect dissipates in a few minutes. Against men in cover the most you get is a pin. The serious guns will instead break whatever they hit and hit whatever they see.