Not at all. I'm talking about the full extended Achaemenid Empire, the one that ruled not just Persia (an enduring and re-forming country) and not just Persia and Mesopotamia (like the Safavids briefly and the Sassanids for a long time).
Rather, the whole enchilada included the fertile crescent, Egypt, Asia Minor and Thrace and extended almost east to the Indus.
Now I can certainly imagine any of these peripheries being lost for some periods, but for later Persian empires to be comparable to the Achaemenid, they probably need to have a Mediterranean cost and a Black Sea coast almost continuously.
If that large a space of southwest Asia becomes an "eternal empire", history going forward is radically different.