Could /sʷ/ be considered a phoneme in Classical Latin?

Words like <suaviter> and <dissuadeo> had the sequence <su> + vowel pronounced as /sʷ/. So in the example words above, the sequence <sua> would be pronounced /sʷa/ rather than /swa/ or /su.a/.

Therefore, just as <qu> makes /kʷ/ and <gu> (+ vowel) makes /gʷ/, could it be said that /sʷ/ is a phoneme, if at least a marginal one?