No, you can just upgrade the instance of SQL Server 2014 to 2017, it won’t affect any connections (except of course during install).
Once you upgraded, you need to change the database compatibility level to the latest 2017 in the database properties in SSMS (SQL Server Management Studio). This is because just upgrading the database engine won’t do this, the database will still remain at 2014 compatibility level until you do this step, but it’s just a matter of changing a setting.