Oh, this is problematic. As far as I am aware, it is supposed that /kʷ/ is a phoneme – a labialised velar plosive. If this is true then /kʷot/ would likely actually have been pronounced as 'kot' (not in an American accent! Think an English accent) because there is no glide, [k] stays where it is.
I've just checked, if this can be correct by looking at words derived from words with the cluster quo. For example French coter from quot-are. No glide there. Also, none of the words derived from Latin quod have a glide. This is evidence that /kʷot/ wasn't [kwot] in Classical Latin
The main question is if the same sound wasn't an allophone of /k/ in front of /o/ and if even more labialisation could have been enough to maintain this distinction. Were there even minimal pairs?