Yes! You can do that very easily with JFBConnect. With our JFBCLike module, you can specify the URL that the Like button is 'for', even it's not the current page or a URL on your site. We do the same thing on our JFBConnect homepage, actually. If you go to the link below:
www.sourcecoast.com/jfbconnect/
The Like button in the upper left corner is actually for our Facebook Page,
www.facebook.com/SourceCoast
We get a lot of Like's that way for our Page, while being able to display a high Like count on the website page.
If you want even more flexibility over how and where the Like button displays, you can use our Easy-Tag, like {JFBCLike href=https://www.facebook.com/SourceCoast} anywhere in an article, template, or other file that will display to a user. JFBConnect will automatically replace that with the correct Like button.
Finally, for Open Graph tags, we have an Open Graph plugin system that can be used for multiple extensions, like Joomla Content, K2, JomSocial, jReviews and more. When you enable the plugin for an extension you have, it will help to automatically set the title, description and image that's best for the current page-view. For even more control, you can add the following tags anywhere on the page to specify the exact title, description or image you want:
{SCOpenGraph title=Best Title}
{SCOpenGraph description=Best description for page}
{SCOpenGraph image=http://site.com/best-image-for-page.jpg}
Hope that all explains, but if you have any other questions, just let us know!
Thanks,
Alex