Old question, but probably useful to others...
Panda3D contains an interface for Awesomium, however Awesomium is not free. This means that there are probably legal limitations for Awesomium to be bundled with Panda3D. That said, at the time of writing there is a very permissive license available for 'indie developers'.
The current Awesomium version (1.6.4 today) seems to have made a lot of changes in the way rendering is handled. The (thin) wrapper for Awesomium in Panda 1.7.2 appears to be for an old version. The quickest, easiest way may be to make you own wrapper.
For rendering, this just means making a ram image texture that is written to by CWebView::render()->copyTo(...);