Well the virus definitions update should still be manageable on dial-up as they are measured in KBs rather than MBs, I managed for most of my 7 years of using avast on dial-up, I only got broadband 8 months ago.
However, if you let it get well out of date (and your program is (6.0.1125 being the latest version) unfortunately not if you have let your virus definitions slide for some time, it will want to download the full database.
It was possible to do that on the old avast 4.8 version, but the virus definitions and how they are used has changed a great deal since then.
So if you can find someone with broadband or local library, local government service with access, internet cafe, etc. I would download
http://files.avast.com/iavs5x/setup_av_free.exe (multi-language version) to CD or USB and install that.
This would have a database much more recent and should hopefully be more manageable on dial-up.