I took a look at the patterns & practices – Enterprise Library official web site (https://entlib.codeplex.com/wikipage?title=EntLib6ReleaseNotes) and I could not find a way to this with EHAB.
Maybe you need switch to Semantic Logging Application Block (SLAB). This one gives you the ability to persist in windows azure tables and others data sources too:
http://convective.wordpress.com/2013/08/12/semantic-logging-application-block-slab/