Well I too have avast on my D drive and for the most part the updates only effect that drive, VPS and Program updates normally effect the files in the avast4 folder. Yes on program updates it may be possible that some of the files in the system folder might change but, program updates aren't that frequent.
You could also do what I do (because I'm on dial-up) don't allow automatic updates, have avast check and ask permission if an update is available. That way if there is a program update you could pause/disable the Deep Freeze, do the program update and enable Deep Freeze again.
Sorry I don't have a clue how Deep freeze works or if this is an option but, avast isn't that much from many programs, you only have to take a look in the C:\Documents and Settings\UserName\Application Data\ folder to see what I mean and this doesn't even include those programs that place files in the system folders. Nor does it take into consideration the registry entries which are in your C: drive.