The poem explicitly features in the story, so I'd say it's pretty guaranteed to have inspired Bradbury ;)

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The SSAATTBB setting of Teasdale's words by Latvian contemporary choral composer Ēriks Ešenvalds is fittingly powerful and a guaranteed source of chills:

https://youtu.be/qwSSVDgY-Sw

The choir I sing in performed the piece for the first time in spring 2022, and against the backdrop of the pandemic and Russia's invasion the words felt incredibly topical and poignant. We're performing it again this spring.

While we're at it, a couple of other ethereally beautiful Ešenvalds settings of Teasdale's texts:

Only in Sleep – https://youtu.be/fvPynMI6Umc (for choir and a soprano soloist)

Stars – https://youtu.be/SK2Rd3qgIGE (for choir and tuned wine glasses!)

I made a composition for string orchestra and male voice from that poem 10 years ago. It's a very powerful poem.

https://soundcloud.com/henrisokka/there-will-come-soft-rains