No. (Unless they are asleep and you are using optional rules from XGtE)
From your quote:
Unconscious ... An unconscious creature is incapacitated (see the
condition), can't move or speak, and is unaware of its surroundings...
A related question (Can a bard grant bardic inspiration to an unconscious creature?) has an answer that says (paraphrased) "Maybe. DM Call". Their reasoning is that Hearing is not specifically ruled out.
I would argue that '... unaware ...' would cover Hearing, and does not need to be singled out. A creature that is unaware of their surroundings is unaware of any sounds, and therefore cannot benefit from Effects that require them to hear something.
Xanathar's Guide to Everything has extra (Optional) rules for being Asleep, which include that Sleeping subjects a creature to the Unconscious condition, but also that they may be woken by sounds. (https://www.dndbeyond.com/compendium/rules/xgte/dungeon-masters-tools#WakingSomeone)
"Specific overrules General" applies here. If a creature is (only) Unconscious, they cannot hear ("... are unaware ..."). If they are Asleep (and therefore also Unconscious), they would fall under the Specific 'Waking Someone' rules (if you are choosing to use the optional XGtE rules), where sounds can awaken the creature. This would imply that the Sleeping creature can Hear, and therefore be affected by Spells/Abilities that require the target(s) to Hear them (such as the OP's example). It may be appropriate to use the Passive Wisdom (Perception) ratings in XGtE's rules to check if the sleeping creature does, actually, hear the Spell/Power.