It won't happen if the ref doesn't give it and VAR doesn't deem it a mistake on the part of the ref.
They've made a rod for their own backs with how ridiculously inflexible this law is, though. Usually, some grey area is present that refs can use to avoid having to give big calls like that against bigger teams.
There is none here - arm, penalty, unless your arm is essentially taped into either your torso or your back. And attackers *will* start deliberately punting the ball into the arms of opponents - why ignore the 5-10 goals a season that can get you?
I anticipate two things will happen at some point.
Firstly, players will start getting more shoulder, elbow and arm injuries, since it simply isn't natural to put your arms behind your back when falling or going to ground around the box. And having the full weight of your body on your arm, especially extended unnaturally behind your back or straight in front of you, is a recipe for these injuries.
Secondly, there will be a ball hitting an arm in the box against one of the FIFA/UEFA's favorite teams (Madrid, Barca et al), and the ref will be forced to give it, causing uproar. The power of these clubs will then force the utterly stupid rule to be discarded.
Too late for Spurs, of course, but then, it always is - we're the guinea pigs for stupid footballing rules, like being forced to play on the final day after Lasagnagate, missing out on the CL after Chelsea won it and now this.