From instrument of the bards which can be used as a bardic focus:
When you use the instrument to cast a spell that causes targets to
become charmed on a failed save, the targets have disadvantage on the
saving throw. This effect applies whether you are using the instrument
as the source of the spell or as a spellcasting focus.
And from the spell compulsion:
Creatures of your choice that you can see within range and that can
hear you must make a Wisdom saving throw. A target automatically
succeeds on this saving throw if it can't be charmed. On a failed
save, a target is affected by this spell.
The spell doesn't outright say the creature is charmed, but also states the spell doesn't work on creatures that can't be charmed, and the effect of the spell is similar to that of a charm spell (and uses the same saving throw to prevent it).
Best Answer
No. The Instrument specifically and only imposes disadvantage on saves for a spell that “causes targets to become charmed on a failed save”. Since Compulsion does not cause targets to become charmed (a specific Condition detailed on page 290 of the PHB), the Instrument does not apply.
A tweet from designer Jeremy Crawford confirms this interpretation of the text: