I agree that it's most probably the air shocks at very low or zero pressure. Parts of the system would be repairable, but if it's the shocks themselves I'd want them replaced.
If you're interested in this bike tell the dealer your concerns and have the problem diagnosed. As part of the deal you should have the repair guaranteed by the dealer. Selling a bike with a malfunctioning suspension is a blatant safety issue. I'd wonder what else they missed.
There are plenty of Road Kings out there, especially this time of year. Maybe it's time to look at a different Road King at a different dealer.