Our daughter knows about the invisible threads, too.
As for the last line, somehow, we've never quite been able to bring ourselves to use it on our kids. It's astonishing and heartbreaking and hypocritical and short-term cruel, but my kids know we (and they) are gonna die, and that nobody really knows when, and all we can do is 1) be careful, 2) be hopeful, and 3) do the best we can with the time and circumstances we're given. I say "hypocritical" since we encourage them to put their teeth under their pillow and put out a stocking for Santa to fill on Christmas Eve, and I've always been happy to fill their wee heads with all the same manner of nonsense described in the rest of that lovely poem. But for whatever reason, I can't bear the thought of adding a dollop of betrayal and deceit on top of their grief and sense of loss should I inadvertently step out in front of a bus or succumb to a surprise brain hemorrhage.
I don't actively recommend this course of action to anyone else; it's an intensely personal and subjective parenting choice that's going to be neither popular nor appropriate for many children. The last thing we want is our kids constantly fretting every time we go to work that we might not make it home alive tonight. But as it turns out, my kids don't do that. So far, the concept of mortality (insofar as they grasp its utter finality, which at 6 and 4 can't be completely perfectly) does not seem to distress them unduly. They get the fact that they won't see their great-grandmother, or their mother's late cat, ever again, and though they miss those dear departed ones, they go on with their lives without dwelling on the tragedy, and though their questions demonstrate that they do think deeply about these matters, they are not fearful and existentially anxious children. They give slightly quizzical looks to friends and classmates who talk about grandparents and pets who "are in heaven now," but we have yet to address that formally.