Eric - why not? A cappella is only a style to produce music. To soothen you: In the Carmina Burana, an old manuscript of the 13th century, you find a lot of bawdy songs, satirizing even the holy mass, sung by students and monks without a band or instruments.
The words "a cappella" are an international musical term and don't mean "in church style" anymore, but - you guessed it - unaccompanied, voices only.
We musicians prefer the Italian terms, so we have to learn them only once in one foreign language and not in several.

Believe me.
Wilfried