I'm hoping to have a common logo/element on the sub sites that link back to the main site. Is that possible?

The main umbrella site has the main overall content - then the sub sites (separate domains) are virtually independent - but are only a click away from the main umbrella site.

I see I can have some content and contacts common through add-on's.

Thanks!

Yes this is possible and depends on the Joomla templates that you are using.
Some templates, use a custom HTML to setup the "logo".
Other templates use "CSS" to define the location of the logo.
Finally other template, use PHP code or setting in the Joomla template to define the location of the logo.

So yes, this is possible and depending on the case, may require to adapt the joomla template to read the logo from a "common" directory.