In my experiences, an PickUp doesn´t use any algorithm until tempo changes. Not that bothers me anyway. Although, I should state that I haven´t tried with any material/source where my aim was that it would sound perfectly clean (i e perfect digital copy). I guess the only one who really can answer that question before purchase would be Elektron Support.
However, it is a bit hard to determine if any of the limitations that the OT got (because it got limitations, that´s certain), are any that will be troublesome for you in the end.
Would you like to elaborate of how you´re gonna try to use an Octatrack?
EDIT: a quick check revealed that whenever you´re recording something into the PickUp machine. It is “untouched” by any algoritm. Until you change pitch. However, if you change pitch and go back to original pitch it seems to actually go back to that “untouched” version again.
I guess that this means that you´re not able to do any tape speed magics, if that is what I think you mean: slower tape speed when recording yielding faster speed in loop playback when raising pitch?
In regard to Ableton, I´m unfortunately unable to confirm or un-confirm any similarities in methods/behaviours compared to the OT. Because I have no experience with Ableton (well last time I used it were many OS versions ago)…