I think they should be fine, providing they are well packed, insulated and provided iwth cool packs (or heat packs as appropriate) 36-48 hour hot/cold packs work best, as you have the assurance if there is a delay, the temp should remain constant inside. With lizards, especially day active ones like bearded dragons, if conditions are not ideal for basking, etc, they will enter a sort of mini-brumation...sleeping or laying still till they are in light again.
When I moved about, I always put my bearded dragon into a box at night while she was sleeping to limit stress (though travel time was in a car with only a few hours of driving instead of over night as in shipping) she was perfectly fine, waking up when the box was opened and light shown in.
Picking up at the nearest depot may be a better ideal for your customer to do, as it does ensure the package gets brought to her home and not cartered around in a truck all day long till they can get to her place. If she has a vehical, she probably be willing to drive two hours to get her new pet (round trip). I was willing to drive 8 hours (round trip) to purchase my first bearded dragon and in fact, 90% of my reptiles. (nearest reptile show is also a 8 hour or more round trip). In fact, only animals out of mycollection of about 21 reptiles that I didn't drive far to get, was the two cornsnakes and texas rat snake a local friend gave to me. All the rest I bought from shows or breeders I drove to (except for two, which were shipped to me).
It certainly could be an option for her to do, though I don't know if it would make any difference in the shipping costs overall.
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PHLdyPayne