Does Fantastical support viewing free/busy information from Google Calendar?
Fantastical mention free/busy information (aka availability) in the FAQ for the Mac version.


  Fantastical 2 does not currently support replying to Exchange
  invitations, marking Exchange events as private, or viewing the
  availability of other Exchange users.


They also answered this question about their iPad version through their Flexibits Twitter account back in April 2014.


  Sorry, Fantastical 2 for iPad won’t let you view free/busy time for
  meeting invitees.


Note they are talking about Exchange, but given it is arguably the most popular source of free/busy information its not a huge leap to assume the same for Google Calendar.

UPDATE 30 March 2016 Flexibits just released a new version of Fantastical for Mac (version 2.2) that includes support for viewing free/busy information. As above, they focus on Exchange support, but Google Calendar is mentioned too.


  ... new in version 2.2 is our spiffy invitee availability view. When
  using a compatible service — such as Google or Exchange — you’ll be
  able to see your invitees’ availability and let Fantastical instantly
  schedule a meeting for when you’re all free, saving you the time of
  coordinating with multiple people. (iCloud does not support
  availability.)