Yes, you can get the content of a web viewer in FMP and, yes, it is supported in FileMaker Go (v1.2.2) with one caveat.
Use the script step: GetLayoutObjectAttribute(web_viewer_object_name;content)
You will have to parse the content to get the displayed value you need which means that the web page should have a fixed format.
In FM Go (v1.2.2), the web page is static not dynamic. That is, the value on the web page will not continually update after opening the web viewer.