Does the linked note from a handwritten task get pushed too?

If a task came from a handwritten note, the pushed task includes a reference to that note's saved PDF. Each app's card has a "Link to notes" switch (on by default). In Todoist the reference goes in the task's description; in Apple Reminders the note's tappable link goes in the reminder's notes; in Google Tasks it's a "Note saved at: Documents/Supernote/<file>" reference (unless you turn on Drive upload — see below); in Asana it's the same "Note saved at" reference in the task's description, with an optional real PDF attachment if you enable "Attach notes as PDFs" (see the Asana questions). The PDF copy is saved locally in your chosen folder (default ~/Documents/Supernote).