Does it make sense to say "recorded an ever-growing collection"?

I would rephrase this as follows: "Some Band has been building a repertoire of original music since 1919." OR "Since 1919, Some Band's collection of original recorded music has steadily grown."

English normally puts an adjective modifying a noun or noun-phrase before but adjacent to what is being modified. Therefore, the normal sense of "_ has recorded an ever-growing collection of original pieces" is that the number of original pieces in that collection is growing. Thus, I think it very unlikely that it could be interpreted as referring to increasing fabrication of physical items that encode performance of some or all of that music, or as referring to an increasing number of performances that have been recorded.

If you are worried about possible confusion among original pieces of music, performances, or physical media, you could substitute "write" or "record from" for "record."

What does sound off to my ear is a slight mismatch between the tense of "has recorded" and the denotation of "ever growing."

I'd suggest "_ has been recording from an ever growing collection ..." That phrasing suggests that the process of recording started in the past, but has not necessarily ceased, a state of affairs perfectly consistent with a still increasing collection of original music.

In short, I am less concerned with the use of "record" as a root verb as I am by the tense chosen.