It's going to depend on how and why the coup fails. The nature of Pinochet's defeat is going to heavily shape how things develop in post-coup Chile. As I see it there's a few possible avenues, each of which would lead to different reactions on the world stage and domestically:
1) Allende calls on the people to resist, they take to the streets, and manage to grind the coup to a halt by massive, largely non-violent show of resistance. This assumes the soldiers who had the stomach to go against their government will not have the stomach to wade hip-deep in the blood of their fellow Chileans; unfortunately given their participation in later atrocities like the Stadium of Death that's a toss up and a risky proposition.
If it plays out like that then you could see similar popular resistance moves against authoritarian regimes spring up sooner in Latin America and elsewhere with the inspiring example of Pinochet's defeat by people power. Allende's legitimacy is going to be assured and politically he'll be untouchable.
2) Allende calls out the people and they show up with guns. I don't know how feasible it would be for enough of his supporters to have enough weapons for this to work but this one could go any number of ways, ranging from bloody street-fighting ending a one day coup to a protracted civil war to the army running over the broken bodies of brave, doomed civilian resisters while prying their weapons from their very cold, dead hands.
Either way it's going to be a bloody mess and even if Allende wins there's going to be reprisals in the aftermath; odds are this will look less good in the eyes of the media and elsewhere if Allende stays in power this way and it'll be much easier for Western media to portray him (falsely) as a communist dictator.
3) Someone blows the whistle on Pinochet & Co with convincing evidence, moving Allende's government to arrest the officers in question. This is probably the most low-key way to avert the coup attempt and would have the least obvious ripple effects since odds are the most that would happen is a short line-item about an attempted coup followed by a lot of military officers losing their jobs, their freedom, and in some cases their lives.
All in all it wouldn't change the situation too much for Allende once the dust settles and likely wouldn't give him a huge boost of popularity like option 1 would or option 2 could.
4) Instead of seeing the civilian population rise up against the coup you have, for an interesting twist, a mutiny against the officers leading the coup and the soldiers take care of it for Allende before anything really serious happens. This one strikes me as the least likely of all options simply because the logic of plotting a military coup implies, assuming the plotters have half a brain (which Pinochet clearly did), they are only going to reveal their plans to units and officers who are likely to follow through with their intentions. As such unless other military units uninvolved in the coup somehow find out in time and try to stop Pinochet, which gets us back into an option 2 scenario, it would be doubtful any of the units "in the know" would mutiny against their orders.