Is it possible to remove an account from Mail, Contacts or Calendars of the iOS Settings app whilst keeping data synced within other categories?
In a word, yes.
Navigate to
Settings &gt; Mail &gt; Accounts
Select the account you want to edit/change
There will be on/off buttons allowing you to selectively sync only those parts of the account you want.
In the screen capture below I have only Mail turned on. I could just as easily turn Mail off and have any combination of contacts, calendars, reminders or notes on.