Well let us make a proper observation:
1. What are genjutsu?
Genjutsu (幻術; Literally meaning "Illusionary Techniques") are techniques that are employed in the same fashion as ninjutsu, requiring chakra and hand seals. However, the primary difference between the two is that the effects of genjutsu are illusory; instead of attacking the victim's body, like taijutsu or ninjutsu, genjutsu techniques manipulate the flow of chakra in the victim's brain, thus causing a disruption in their senses.
Genjutsu is created when a ninja extends their chakra flow through the cerebral nervous system of their opponent to control their mind, thereby affecting their five senses.
2. How can a genjutsu be broken?
To combat the effects of genjutsu, there are several options:
a.The ninja needs to stop the flow of chakra in their body, and then apply an even stronger power to disrupt the flow of the caster's chakra; this is called Genjutsu Dissipation (幻術解, Genjutsu Kai). This can also be done by an unaffected ninja by applying a sudden surge of chakra into the affected person. In addition, tailed beasts can break their jinchūriki out of genjutsu in a similar fashion if they have a good enough cooperation, as seen in Killer B's case.
b.Another is through intense pain not caused by the genjutsu and utilising the resulting pain to bring their senses back in order (of the first two options, the latter seems more effective in most situations, or at least is the easiest).
c.Another option is accessible only to Sharingan wielders. Members of the Uchiha clan can break or see through genjutsu using their Sharingan. Breaking Tsukuyomi is possible with an ordinary Sharingan, but requires a lot of skill.
d.Sharingan wielders can also use their dōjutsu to liberate any ally caught in an enemy genjutsu by casting their own genjutsu on them, literally breaking into the illusionary world they are imprisoned in order to free them. This can be achieved through eye contact alone.[3]
e.Ordinary people can sometimes train their eyes (without Sharingan) to break genjutsu through unknown means, like Deidara.
f.One can prevent a person from casting genjutsu using obstructive techniques like the Hiding in Mist Technique to prevent one from being trapped by an ocular genjutsu as Zabuza demonstrated against Kakashi.
e.In the anime it was shown that strong smells like that from the Chilli Pepper Bombs, can counteract genjutsu.
In spite of these methods, some forms of genjutsu like Itachi's Tsukuyomi and Shima and Fukasaku's Demonic Illusion: Toad Confrontation Chant may not be broken easily, either due to their near-instant effect like the former, or their ability to render one unconscious and paralysed altogether like the latter. In addition, one must realise that he or she is under the effects of genjutsu before attempting to break out of it. This can be done by observing the changes in one's own chakra like Karin's chakra-sensing ability.
But Because genjutsu affects activity throughout the Prosencephalon structure of the brain, humans, dogs and other species of mammal are therefore all affected by genjutsu; however, the kikaichū, like all insects, lack such a structure to their brains, and so do not even notice it: as Shino Aburame put it, insects are ruled almost solely by five powerful senses alone, which makes them immune to genjutsu and gives the Aburame clan an ability to detect it when nobody else can.
CONCLUSION: IF ur caught in TSUKOYOMI ur practically dead.
3. Now lets consider Nagato's special cases:
a. Nagato share the vision field of the six paths, but is putting one genjutsu on one path is enough to put them all in genjutsu? Remember genjutsu needs to controls one's chakra system, so is controlling one paths chakra system system enough to control the chakra system of all the paths? I dont think so as the paths share only the same field of vision nothing else. Also nagato can just stop transfering chakra to a path and 'restart' it to get it to normal, as they are puppets not living things and can feel pain.
b. Nagato can do a non mammal summon like a reptile or a bug to use their field of vision and keep his eyes closed to aviod genjutsu. This wld work as only mammals are affected by genjutsu not others.
c. The cyborg path may be immune to genjutsu as he is part machine.
Side: Note Itachi said that only a clansman can break out of his Tsuki (on his own) but is nagato with his six paths?