Well, if Avast has to wake to do it's streaming, or wake to do an update that removes all the power savings from sleeping. Avast could trigger to update when the computer wakes from sleep, or start streaming when the computer wakes from sleep. Then if it goes to sleep disable the streaming until the computer wakes and then re-enable it.
I don't believe that it does otherwise I'm certain we would get many more posts about this.
This system is on all day, but I have fairly tight power settings to go to standby monitor 5mins; HDD 15mins; system standby 20mins. When I bring it out of standby I can check the C:\Program Files\AVAST Software\Avast\defs folder and look for the 99999901_stream folder and the pkg999999999999.bin files received usually coincide from closely after coming out of standby.
My win7 netbook spends most of its time in standby and I never switch it off - I have just brought it out of standby/sleep and I see the 15100501_stream folder just created and all of the pkg9999999.bin files created within the last minute or two.
So it isn't coming out of standby/sleep either. I'm not sure what is going on with your system.