Late follow-up of this unresolved topic: check if the current page has a parent.
https://wordpress.org/support/topic/if-page-has-a-parent/

I found a solution, a bit complicated but it works.
Could be useful to other people…

1. Loop to get current page parent
2. Store parent in a var
3. Pass var to conditional

[loop child=this]
  parent slug in the loop: [field slug]<br>
  [set parent_slug][field slug][/set]
[/loop]

[pass vars]
  Parent slug passed in var: {PARENT_SLUG}<br>
  [if pass='{PARENT_SLUG}' empty=false]
    Has parent!
  [else]
    No parent…
  [/if]
[/pass]