Do dishwashers depend on their discharge line running up from the drain
pump and forming an up-loop before falling down to make a connection to
a drain line? Do they depend on this arrangement to prevent fill water
from draining unintentionally from the machine?

No. In a normal installation the drain for the sink is above the water
level in the dishwasher so the machine will not drain in this manner. The
loop negates the need for an air gap. However in your case the loop would
probably help prevent such drainage. Your installation dropping thru the
floor into the basement may well create a strong siphon action preventing
the loop from functioning as it should. An air gap may be required to break
the siphon. A trap and vent is needed in the basement. A vent can be
created using a one way air valve so the vent does not have to extended thru
the roof.