And if this conversion is done not locally, but via SaaS, that's just an implementation detail. I believe there's precedent for this (which I cannot find at the moment), but if this was not the case, then you could not touch any document you did not have copyright on using e.g. Google Docs.
Edit: Found the precedent where time-shifting (i.e. video recording) was found to be non-infringing, regardless of if it's done locally or remotely [1].
https://en.wikipedia.org/wiki/Cartoon_Network,_LP_v._CSC_Hol....