re: Is it possible to link the existing Users with a custom Role I have already in place instead of creating separate users for the Connections plugin?
Sorry no. The Connections entries are separate from WP Users. The best that can be done is use the Link extension. User would be able to add and maintain their own entry in Connections but the info would still be separate from what you already have in the WP User Profiles.
Now you could possible use a WP USer CSV Export plugin to get the data out then use the CSV Import extension to get the data into Connections. Could be a workable solution for you if you want to use Connections.
Hope that helps!