The LT3042, LT3045... (all positive LDOs of that family) note that some fraction (1:400 or 1:500, depending on max current) of the output current is sourced from the ILIM pin.
Given that the LT3094 is from the same family and the block diagram looks similar e.g. to the LT3042 block diagram, I'd expect it to sink a fraction of the output current (probably 1:500) at its ILIM pin.
Is there any indication the the LT3094's ILIM pin can not be used as a current monitor?
Also, do I understand it correctly that exceeding the output current limit will result in a decreased output voltage for resistive loads (so that the current limit is met) and not in a shutdown and restart after some delay? Although it seems like this is true from the block diagram, there is no written documentation about that behaviour which I can find.
You're correct. When the part hits the current limit, the output voltage will drop for resistive loads.
ILIM cannot be used to as a current monitor. The internal circuitry is different from LT3042.