Templates for Connections are similar to themes for WordPress, they “simply” change the appearance that your data that is displayed, so there is nothing being ported. So the simple answer is, yes, your data will “port” over.
None are really the closest … maybe the cMap template, the gradient can be turned off. So can the logo. The bio details would actually be shown in the bio content tray … the user would have to click the link for the info to be shown in a slide down effect. The link names can easily be changed to be applicable.
Another possibility, since you are not showing any images, is the Slim Plus template. The image can be turned off and it defaults to 20 entries per page. A user would have to click the entry name to reveal the details. Not sure how important being presented without any user interaction is to you but it would provide a nice clean look that would fit nicely with your theme.
Hope that helps!