I think not. They are independent update features. You can have a dial-up and the push update feature working togheter.

For the first question: you will set the system check for a live connection each 40 seconds if you did not check that option. When a connection is detected, system will wait 4 hours to next check.

The second: no, it won’t disable the message.
You must change your avast4.ini file settings. See: http://forum.avast.com/index.php?board=2;action=display;threadid=1647;start=0

On the AAVM section:
SuppressUpdateErrorInfo=1 will suppress update error message (not the update itself).
SuppressUpdatedInfo=1 Suppress the small blue info window in the notification area of your desktop on updating.