Is ‘always-on-the-wall fly’ a grammatically correct phrase?

Technically, adverbs can modify a preposition.

https://www.merriam-webster.com/dictionary/adverb

And adverbs of frequency can modify a modifier.

Ex) Always-green plant

And prepositional phrases can be followed by a noun they modify with hyphens.

Then, can a fly which is always on the wall be expressed as ‘always-on-the-wall fly’?