You do still have a requirement to meet either your six month proficiency check, or six approaches (plus holding tracking, etc) in six months, and this must be logged. It must also be done under actual or simulated instrument conditions, and the approaches themselves must be flown in actual or simulated instrument conditions to minimums (per the FAA Chief Legal Counsel). These approaches must be logged as such in order to meet the requirements of the regulation.
However, you need not keep those records in a "log book." You can simply keep a record of the PT/PC session that you get from the Instructor/Evaluator at the time of the sim session.
Though there may be no formal requirement to log specific items, I believe it is a good idea to keep a current log book for whatever [unforeseen] future purpose you might need it. While your current job may be secure NOW, you can't rely on that next week or month or year. Also, if you buy or rent an airplane, an insurance company may ask you for proof of recent experience...