Are there any Rover.com consequences to booking a stay after it has already begun?

SInce its a repeat client I would just create another booking for them. It gives them 72 hours to confirm the booking. And dropping a note to support via the Help button is probably a good idea or just call them.

If something unexpected happened, I'd guess insurance and support wouldn't cover it.

When I've faced a similar situation (repeat stay client traveling), what I've done is offer to book at drop-off, or if that absolutely can't be done, ask them to book while waiting at the airport (five minutes away) and remind them if they can't do it online they can book over the phone and give them the #.