I wonder at what part of the MySQL upgrade it fails at... We should add a bit more reporting during upgrades so we can figure these things out easier
What plugins do you have installed?
If the plugin doesn't support 2.0.0 then it might break the Geeklog install. To get around this I would disable all plugins that are not part of the core.
A few people have reported issues upgrading from 1.8.2 to 2.0.0. On my sites I did not have any issues and the stock install of Geeklog upgrades fine.
Depending on what you say about the plugins, for me to look into this further I will probably need a copy of your site to test.
One of the Geeklog Core Developers.