"Off the shelf" isn't a constraint here, sort of the opposite: I'm trying to imagine the space of things that are physically possible but not yet commercially mature. Theoretically, higher temperatures mean more possible efficiency. That's the one ray of hope in otherwise dismal efficiency figures that are currently only viable, as you point out, if the heat is ~free.
I think you might be conflating a few things here. For a cycle to produce electricity, that's correct. But the mechanism of absorption chillers is fundamentally different. The chemistry of the materials and their phase change temperatures are definitely a constraining factor. Could you, in theory, develop some other absorbent/refrigerant that works at those higher temperatures? I suppose, but I would suspect there are much easier ways to get efficiency gains.
Typical refrigeration COP (Coefficients of Performance):
Absorption refrigerator: 0.6-1.2
Compressor refrigerator: 1.5-4.0
Estimated TES economic advantage: 1.1-2.5x
Conclusion: yes, absorption refrigeration is probably inefficient enough to make it a long shot in this application. The only way I can see it becoming viable is if extremely hot TES can completely change the efficiency game, and then only just.