It wouldn't be particuarly hard for avast to operate this system without having the key for the CA leaving your machine.
Re:Avast’s man in the middle
by venomsnake on Sunday December 13, 2015 @03:33PM
(#10727800)
That won't help when they send part of the plaintext home. Which any antivirus program does from time to time
There are other problems. I am not sure where the third party doctrine will stand, but you are trusting all of your secure connections to a third party with full consent.
If avast get subpoenaed and their software has called home, which any antivirus does - they must collect new samples all the time - this could spell trouble.