Well, it does include material about the Crucifixion; on the other hand, that doesn't appear until the third stanza and afterward, so I don't think it's an ideal match for the day.
There's nothing "wrong" with doing "Adoro te" any time of the year, but if I were to use a traditional Eucharistic text on Palm Sunday I'd lean more toward an "Ave verum corpus."
I think it might highlight something that is often overlooked.
On Palm Sunday, the Passion has traditionally included all of Matthew 26, which has the preparation, Lord's Supper, and institution narrative.
This was the only Sunday of the entire year to include the Gospel account of the institution of the Eucharist, and I think it still is (with the corresponding accounts from Saints Luke and Mark). On Holy Thursday the Gospel is of the washing, with the institution narrative from Saint Paul.
Amazingly, in the 1962 Missal (but not the pre-1955) the 'synoptic' institution narrative is completely omitted...
Extraordinary Form (EF) Graduale Romanum 1961 CO Ant Pater, si non potest hic calix transire, nisi bibam illum; fiat voluntas tua.
(Gregorian Missal (ABC=Matthew 26:42 (Father, if this cup cannot pass away unless I drink it, thy will be done.)
Ordinary Form (OF) Graduale Romanum 1974 CO Ant same as above plus these psalm verses Psalm 21*, 2, 3, 5, 7, 15cd, 17ab, 17c-18, 22, 23, 24, 28, 20c-31a, 31b-32 vel Psalm 115*, 10, 11, 12, 13, 14, 15, 16ab, 16c-17, 18, 19
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