No - because the homepage is not 'your' homepage - it is 'the' homepage.

while there may be elements on there if you are logged in - these can all be accessed via the 'My ebay' section.

The homepage is ebays shop window. Today - they are promoting ebay live in a big way. Next week there will be some other promotion.

But there is no way to turn it off via a preference - because its simply advertising on ebays homepage.