@vmak -- I think that making that connection would be dicey, but I understand wanting to maximize your time in Granada, a city I enjoy much more than Madrid. All the steps below would have to go smoothly for you to make it:
Your plane arrives on time and you get off the plane quickly, making a beeline for passport control.
No long lines at passport control.
Your baggage arrives quickly and you have no customs issues.
You can make your way to the airport Metro station quickly and buy your one way ticket to downtown with your chip-enabled credit card (or Euro cash) quickly. On my last trip there in 2015, my primary chip card didn't work in the machine and I had to use my secondary chip card. I seem to recall there's a staffed ticket booth, so you could buy your metro ticket there if the line's not too long.
You become familiar enough with the Madrid Metro map and routes to know that you need to transfer Metro trains twice to get to Atocha RENFE station, hauling your luggage up and down escalators or stairs both times.
You actually get off your Metro Line 1 train at the Atocha RENFE station (and not the next prior plain "Atocha" station).
You make your way from this Metro station into the actual railway station.
You know your initial train number and destination (likely Sevilla Santa Justa or Cárdiz) so you can find the right platform.
The entrance to your platform at Atocha RENFE will likely be upstairs via an escalator, and you go through airport-like security. Show your already purchased ticket and passport.
Once you get through security in time for your train departure, you can breathe a sigh of relief and relax in the lounge until your train is called. When it is called, hustle on down the escalator to the real platform so you can find the right train car (car number and seat number shown on your ticket). You'll be able to buy food on this first train.
Your connection between arriving at the airport and departing on your desired train is something I would try if I were doing this myself, sweating my way through all of these steps, as I've flow into MAD airport a few times, taken the Metro a few times, and taken trains from the Atocha RENFE station a few times. And I speak a fair amount of Spanish so I can ask questions of passersby or officials.
If these are all new to you, you'd be better of just forking out the big Euro bills and pay for a taxi from the airport to the Atocha RENFE station. Any taxi driver there will know "Atocha RENFE" -- just make sure he takes you to the station instead of the nearby Atocha plaza.
As for RENFE, the Spanish passenger train operator, being able to honor your discount-priced ticket if you don't make your selected train, don't count on it. Their website says no cancellations and no changes, but you could try to plead your case at the RENFE ticket office. I wonder what other, more regular RENFE users have to say about this.
Madrileños and others who have spent even more time there may have other thoughts and perspectives.
Best of luck!
