I'm not sure that would work well as it would need to understand the cycle of the (unwanted) backing - i.e. in a simple backing track there might be a kick drum, then snare, and the system would need to know where those 'should' be in relation to the backing - I don't think this would work that way - particularly due to the way that it's achieving the removal of the unwanted noise (altering the response of each band of frequencies).
I'd think it would be possible to create something that would do what you're looking for, but it would be much more complex than the above (and -way- beyond what I'm capable of at the moment, maybe in a couple of years I'll be able to do something like it).
I've had more luck with taking the backing and using phasing to remove it from different sections of a song - if you get a track where the backing is simple, sequenced and samples/repeatable synths (so that the sound is identical each time it happens), then it's possible to take that non-vocal section, and align it with the vocal section on another track and reverse its phase to get cancellation; You have to be precise and get lucky in terms of the rest of the track, but it is possible. There is, of course, the old stereo swap and reverse phase trick which removes everything that's not panned centrally; that can get you a lot of mileage.
As mentioned, though, in another comment, getting hold of acappellas/stems can be much better, and having listened to some of some classic tracks, you can learn a lot about production in a short time by doing so.
I'd think it would be possible to create something that would do what you're looking for, but it would be much more complex than the above (and -way- beyond what I'm capable of at the moment, maybe in a couple of years I'll be able to do something like it).
I've had more luck with taking the backing and using phasing to remove it from different sections of a song - if you get a track where the backing is simple, sequenced and samples/repeatable synths (so that the sound is identical each time it happens), then it's possible to take that non-vocal section, and align it with the vocal section on another track and reverse its phase to get cancellation; You have to be precise and get lucky in terms of the rest of the track, but it is possible. There is, of course, the old stereo swap and reverse phase trick which removes everything that's not panned centrally; that can get you a lot of mileage.
As mentioned, though, in another comment, getting hold of acappellas/stems can be much better, and having listened to some of some classic tracks, you can learn a lot about production in a short time by doing so.