It depends. Teeth go through stages of pain. First the nerve is dying and highly inflammed. You definitely do not want to be poking around without anesthetic at this stage.

Next the nerve dies and the pain goes away. People often feel a sense of relief at this point because they want to believe the problem just resolved itself.

Some time later an infection forms at the base of the tooth, causing pain because of an increase in pressure in the jaw. This can be excruciatingly painful but the source of pain isn’t the tooth itself (the nerve is dead), it’s the jaw. At this point someone could theoretically do a root canal without anesthetic. It wouldn’t be pleasant but it also wouldn’t cause the insane kind of pain you’re thinking it would cause. That being said, never do your own root canals or have someone who isn’t qualified do one for you. They’re extremely technical and require exquisitely trained fine motor control and having a non-professional do one will cause more problems than they solve.

Source: I do root canals for other people and I would never do one on myself