I would say that Orsino's next words rather make Elizabeth's case:

If music be the food of love, play on.
Give me excess of it, that surfeiting
The appetite might sicken and so die.

And indeed Orsino's love for Olivia could hardly be considered a "healthy" sort of love

In other cases, attempts at poetry are considered laughable, or not signs of a true love:

Among them,

Orlando's poetic verse to Rosalind in As You Like It is mocked by everyone including his own love (until she finds out that he penned it, and then the important thing is him, not his verses.)

Celia: Didst thou hear these verses?
Rosalind: O, yes, I hear them all, and more too; for some of them had in them more feet than the verses would bear.

In the same play, the melancholy Jaques refers to love poems as foolish: "The lover/Sighing like furnace, with a woeful ballad/Made to his mistress eyebrow."

In Midsummer's Night's Dream, Lysander's rhyming words to Hermia (not that they don't all rhyme in that play) lead her to say:

"Lysander riddles very prettily
Now much beshrew my meaning and my pride
If Hermia meant to say Lysander lied..."

In Much Ado, Benedick and Beatrice write love poems to each other, but their efforts are mocked within the play, as Benedick confesses that

"I was not born under a rhyming planet,/Nor I cannot woo in festival terms."

In Two Gents, the fickle Proteus and foolish Thurio employ poetry to ensnare Sylvia, and only further her disgust with them. She appreciate's only the efforts of the man she is already in love with - Valentine.