>Has anyone seen or used an Continuous absorption AC system
>(compressorless like the fridge)?

In the commercial version.........

Large units capable of making 40 to 50 degree f chill water for cooling
large facilities use steam, hot water or are direct fired from nat gas or
oil. The Japanese have tried using volcanic thermal water from the ground
for making chill water for fish processing plants.  GM tried to cool the
Oklahoma City assembly plant offices with solar source hot water absorption
units (failed).

I have seen solar powered (read tiny) window cooling units in Japan.  I
assume they are absorption units.
The large plant type units are energy hogs.  Example; If you have 1 energy
unit input to realize 1 cooling unit output from a conventional cooling
plant, in an absorption plant you will input 4 to 10 energy units to realize
1 cooling unit output.
Absorption is efficient only when you have available a free or cheap energy
source.  There is a local large urban hospital complex that has a source of
free well head nat gas and they use steam powered absorption for chill water
source cooling.
Japan has improved on the technology and has (Hitachi) very efficient direct
gas fired commercial units.  The byproduct is hot water for domestic use or
heating.

It appears to be magic.  212 degree f. steam or large gas burner heat goes
in one end and 40 degree f. chill water comes out the other.  There is no
visible moving parts.  Technically the refrigerant is distilled water.
Works under high vacuum.  The transfer fluid is a very strong mix of lithium
bromide.
Eckie 'Ruined more than one pair of boots in LiBr' Prater