I'm not positive on that, but I wouldn't think so...
So, this works:
Database.dbo.TableName
but this doesn't work:
Database.TableName
As long as the currently logged in user has access to both databases, you can access both. And as far as my tests have shown, you don't have to worry about what database the connection string is using; when you use the full database scope syntax, SQL Server will find the correct table, no matter what database it's in.