I know that there is this 60 day rule for COBRA (and it is actually 60 days from when you are notified of eligibility, not from the qualifying date), but in our case, they couldn't get us enrolled, Megacorp ended up paying extra months to avoid any penalty, and now it is nearly a month since the clock was reset and the benefits company still has us in limbo. Both times, we have the eligibility letter, but the benefits provider can't, in their words, "get the button to show up."
If your child does go this route, even though they are unlikely to have it as *bleeped* as we have, they need to know that they will likely have to pay and be reimbursed because they won't be able to give an active insurance until after the premiums have been paid. We have found that providers that we have used for a long time just assume the info is the same, but once a claim gets rejected because that individual isn't covered, they really want to know what is up and would rather like their money. New providers will try to run the insurance card and see right away that it isn't valid.