hmm... i am currently working on a publication totally not related to my PhD. i'm not doing it all alone though, but together with my boyfriend. i told my supervisor about it and she likes it and encouraged me to go ahead with it but did raise some cautionary words about it not supposing to distract me too much from my PhD project. but, frankly, that's exactly what it is doing - at the end of the day, if it's going to be up to standard for publication it is going to take a lot of work.
if you go ahead with this i would be interested in your experience!