I added a to-do offline (no internet). Will it still get to my Supernote?

Yes. If a change can't reach the cloud right away, the app remembers it and automatically sends it once the connection is back — so a to-do you add, complete, rename or delete won't be lost. It then re-checks to confirm the change landed. (Deletes are handled especially carefully so a momentary glitch can never silently wipe a list.)