Not by default, but PM2 can do so using a startup script:
PM2 can generate startup scripts and configure them in order to keep
your process list intact across expected or unexpected machine
restarts.
After generating your startup script (read also this comment), take a look at pm2 save:
Once you started all the applications you want to manage, you have to
save the list you wanna respawn at machine reboot with:
pm2 save