Hi Fran,
I think the huge file size of the more recent versions of Band in a Box is due to all of the Real Tracks (I think that is what they call them; the sampled loops of real instrumental accompaniment). But given the fact the apps like Garage Band, Music Studio, and many others can easily record and playback multiple tracks of sequenced and/or audio tracks with no problem I see no reason why an app couldn't be written to provide auto-accompaniment/arranger capabilities. The Easy Band Studio program I mentioned for the Android O/S does a great job for what it is. The sounds aren't at the level of even an entry-level arranger keyboard. But for working out tunes, i.e. trying different chord progressions, styles, tempos, etc. it is just fine.
Thanks for responding,
Dave