Does this passage teach us anything more about their characters?
No, from the moment Melkor made that rash promise we knew he'd regret it!
Could it ever have worked betweem the two?
No, no real connection other than shared evil. Ungoliant was too much of
a low-order creature to have a real relationship with. Some of Melkor's
other hench-creatures (e.g. balrogs) seem to respond better, and Sauron is a
genuine ally and servant.
Ungoliants hunger makes me think of very ancient religions.
Ifthe Silmarillion was a real mythologie in our world, I would guess that
Ungoliant was a survivior from a predecessing pantheon who had been included in
the current one.
Her description certainly make one think of truly ancient, dark
legends.

Excavated artifacts show how Gondorian warriors relaxed in the barracks while awaiting their moment of glory, contemplating heroic feats of their ancestors.
Urn by Christoph Niemann, The New Yorker Magazine, Aug. 9 & 16, 2004.