I don;t see pursuing a disinterested woman as a particlar waste of time as long as she's on the backburner and you are spending 80% of your time on something that seems more fruitful.
Like for example if you just like talking to this chic, she can be a good stress reliever so that you don't dump all over your new girls. You can also use her to cuddle with when you feel bad, and she may provide useful advice. OTOH, if you can't even get advice on a hairstyle or cuddle time with her, then it's probably time that is best spent someplace else. It is always possible such a woman will become attracted over time, but it's so unlikely that I would just consider it a loss and use her for other purposes like helping me meet and pull new chic.
I used to do this a lot and these chicks introduced me to new chicks a lot, helped me in various areas, provided social proof, etc. If a chic isn't useful for any of those things, and you aren't doing her, then she is of no use at all and just wants you to go away.