I have noticed that no matter what timezone I set in User Preferences:
... all dates and date times displayed in Odoo are shown based on the SYSTEM TIME of the underlying operating system the client uses (mainly Windows for my users).
The tooltip for this field states: "The partner's timezone, used to output proper date and time values inside printed reports. It is important to set a value for this field. You should use the same timezone that is otherwise used to pick and render date and time values: your computer's timezone"
Is there any other logic in Odoo that is affected by the setting in this field?
Excellent question in my opinion. I am seeing the same thing as you: even though I change this field, Odoo will ignore it and just use the system time. So in other words, what is the use of this field if Odoo ignores it?