I don't really know the best way to let you know but there is at least one compatibility issue with Connections and WPMU - that is the images aren't saved/loaded from the correct location and thus it doesn't really work as expected.
We migrated from a single site instance of WP to a WPMU. As you know on a single site instance all content is stored in /wp-content/... So the images from connections are in /wp-content/connection_images
However, that path system won't work with WPMU because each site within the WPMU install has it's own directory underneath wp-content where it's files are stored. For example:
Where 1 is the id of the site on the WPMU network.
The problem here is that the code for Connections is setup to define a constant "CN_IMAGE_PATH" and "CN_IMAGE_BASE_URL" that simply use the WP_CONTENT directory like so:
define('CN_IMAGE_PATH', WP_CONTENT_DIR . '/connection_images/');
since these are constance we can't really do something like:
define('CN_IMAGE_PATH', WP_CONTENT_DIR . '/blogs.dir/' . $blog_id . '/files/connection_images/');
The same will hold true for custom templates for each site I imagine.
Thus unless someone wants to modify the plugin to be smarter and identify if it is in a multi-user instance or a single site instance I don't think this can work completely with a WPMU install.
Please correct me if I am wrong.