Will A from Every Day ever die?

Every day, A wakes up in a different body and lives that person's life. We don't know why or how this happens, but A gives us some information about their experience. A tells Rhiannon that as a baby, they thought everyone lived like this. At age eleven, when spending the day in the body of a boy on a ski trip, they got in an accident and broke that person's leg. This prompted them to consider the idea of death:

And if he’d died . . . I wondered if I would have died, too. There is no way for me to know. All I know is that, in a way, it doesn’t matter. Whether I die or just wake up the next morning as if nothing happened, the fact of the death will destroy me.

So we see that A ages, and perhaps therefore could die of old age once they grow old. But we don't really know for sure how A exists and whether A is immortal or not.
When A meets "Reverend Poole" later in the story, A realizes that there are others out there, with the potential power to stay in the same body for more than one day. The person possessing Poole says

You have no idea the power that you possess.

This leaves us questioning if that power includes immortality, but A is very careful about not harming the bodies they possess and does not want to interfere too much. Levithan does not give us a clear answer.