Yes, and no.
Like all advanced trees, many frangipani trees grow well in nature by themselves, without any human help. While almost all advanced frangipani trees ‘survive” by themselves, many of them go through stages of poor health. Observing, noticing problems and acting is more about keeping a frangipani tree healthy and looking good as opposed to keeping it alive.
As for small frangipanis, when things go wrong in the initial years, consequences can be more severe, so care is more important.
At Efrangipanis, we have many frangipanis in the ground. While we rarely water or fertilize any of them, we spray two or three times a year against frangipani rust. As for our 1m tall frangipanis in the ground, our biggest challenge is stopping grass and weeds from growing over them and smothering them.