I can see the Sassanids conquering Egypt, bu I don't think Parthia was up to the task for a few reasons:
*Terrible logistical inefficiencies, Tacitus notes they were not even able to advance much further than into Armenia when at war with Rome owing to vastly inferior logistics.
*National instability: their subject kingdoms and peoples were always of dubious loyalty, reading Suetonius and Tacitus we see the Parthians' war efforts constantly sabotaged by risings of subject peoples of revolts from within their own royal family.
*Natural barriers: Egypt has always been protected by the Sinai in the East. Typically naval support is needed to assist in an invasion of Egypt, which Parthia never had. Combined with their weak logistics, the Parthians could not sustain an invasion of Egypt.
*Egypt also had its own quite capable military and under the highly dubious circumstances that the Parthians made it to the Nile they were not the sort of army good at besieging the many large cities in Egypt. If the Egyptians could prevent the Parthians from taking cities, they could prevent them from having free reign to forage for supplies and the Parthians would be staring starvation in the face.