I think we cannot say where or not the Alpha Legion is "really Chaotic", because we have not probably defined what "really Chaotic" means.
For example is "really Chaotic" defined by the worship of the chaos gods or just their acceptance of their existence?
For if that was the case the a special character like Fabius Bile would not be "really Chaotic" as he doesn't even accept that where are gods.
And by that definition I would not confirm that the Alpha Legion in general is "really Chaotic"
Sure we have not really nice examples of some members of the Alpha Legion going "really Chaotic"
But the legion in general? No information can confirm or deny this.
Now some will point out the rules and some of the nice art that is available.
To that my first question would be
Do you really think that GW would risk creating a great imbalance in term of gameplay by giving the Alpha Legion a different army list?
Would denying the Alpha Legion the use of some units not hamper them?
Or what if Alpha Legion got really good units to replace the lack of unit X?
After all GW has not given the loyal and heretic more or less similar rules to prevent imbalance?
I also have not see a single Alpha Legion specific model release for 40K
And all the models that are showcased only have the bare minimum done to them.
A paint job and the icon from a transfer sheet.
If I strip the models of paint, there would be not indication whatsoever that they where from the Alpha Legion.
Just take the Dark Apostle. Without a paint job does in any way make you think Alpha Legion?
The we have the art.
Each time I talk to someone from GW about the art and lore.
I am told that it more a rule of cool than the lore that what drives the creative process.
So we should not use art to determine what is cannon in the lore.
So from this I would not say the Alpha Legion is "really Chaotic" if we go from the definition of worship or acceptance of the gods.
Nor would I say that it disprove as we do not have enough information about the legion as a hole to make any claim.
One could also defined "really Chaotic" but the use of chaos power and knowledge.
In this argument I would say that Alpha Legion is very much "really Chaotic"
From story and codex there is a clear indication that nothing is taboo for the Alpha Legion to use or do.
To them the result is all that matters, the means to the end are something that is to be use and discard.