Just a clarification - Google only implemented push notifications in their API about a year ago (
http://googleappsdeveloper.blogspot.com/2014/06/introducing-new-gmail-api.html), and AFAIK there aren't too many apps yet that implement push data (Gmail pushes
notifications, and polls data). Gmail has utilized polling for quite some time; I'm not going to get into a discussion about their half-assed implementation of "Exchange" FWIW...
There are no Mac desktop clients that use MS's newer "streaming" Exchange notification system (pushing notifications, pulling data at polling intervals). We're "stuck" with EWS on Mac clients so far, and that includes the new Outlook app. MS was supposed to move to streaming EWS as early as 2009, and it seems the Mac client apps are waiting for the rest of MS to catch up IMO.
Also, MS has been moving its clients to the "streaming" system for about 3 years now, with polling intervals set up in the client - about 1 minute is the smallest interval, and an IT person would have your head if you set it up that way in an office environment.
Stop thinking of "push" in terms of email or calendaring - it's the notification that gets "pushed", and then your client will eventually pull the data. MS's blogs explain this in excruciating fine detail.
I have an Outlook.com and an Office 365 account for my personal email - with the default settings, I find that my calendar events and email messages are mapped in almost real time - I'll have an iPad/iPhone, the web interface(s), and Outlook 2013 (on Win 8.1) or Outlook 2016 (O365 account only), and find that moving one IMAPI item in one interface leads to updates on the other platforms within seconds (with my iPhone/iPad) on cellular (not wifi). The Outlook 2016 client takes a minute or two to update emails (likely due to the EWS connection, I'm guessing). If you want something faster than that, well, OK then...