Can a member of the SQL server 'sysadmin' role login to any database?
A sysadmin can use any database and also specify any database in the connection string. The special dbo user is used whenever a sysadmin does anything inside a database.
If you failed to connect to a specific database, then I'd say that the database doesn't exist (or is inaccessible) or you aren't a sysadmin. :-)
(Sorry I don't have something to point to the specifics about having a database in the connection string.)