Hi imaxinant,
the background of a widget cannot be transparent, but you can resize the page of the widget in iAd Producer. This will produce the same effect if you embed the widget in your iBooks Author page rather than let it play full screen.
At the top left of your window when you're working on your project, you should see an Overview button like so:

Click on this to get a view of all the pages in your project. On the right hand side will be an option to change the page size. Change this to custom and resize it to the full extent of the content in your widget.
Now, create your widget and drag it into iBooks Author. Resize it so that it is as big as you need it to be.
In the Widget panel in the Inspector, turn off Title, Background and Caption in the Layout section and then, in the Interaction section, select Plays on Page and check Plays Automatically. If you don't see these options, you'll need to update your iBooks Author software to the latest version.
I hope that helps you.