ABBYY FineReader supports Hebrew and Arabic since v. 11. But I'm afraid same script is not enough. For example FineReader has 3 versions for Armenian. All three use same scripts, different orphography and slightly different vocabulary, but if you set wrong language drop in quality is dramatic. So I'm not sure if Arabic OCR would work good for text in Farsi (Persian).
FineReader provides 30 days full trial, and I think it's worth to give it a try.
You may try to approach ABBYY and check if there are any plans on full support of Persian in coming future.
And trying to train Teseract seems like good idea to get free/open source OCR for Persian, if you can get enough resources on that. But I can't comment on how well it will work with RTL scripts especially with Nastaliq/Naskh when letters and words are not separated from each other.