I hope I'm not too late in getting a response to you.

My advice in this situation would be to let them fulfill the delivery requirement. Normally, it would be ideal for the unit to gradually move to room temperature, and if it was mine, I might insist. But I don't see any particular reason why a quick power-on would cause any damage to the unit.

If you can avoid it, I would. But if you can't, it's not likely that the unit will suffer long term damage as a result.