Do they? West Asia in total has 300 million people, 40 million more in Afghanistan and 200 million in Pakistan but I wouldn't call Pakistan part of the "Iranian realm" especially not if by itself it carries so much of the population of the region. But I don't disagree that a lasting Achamenid empire can't full the requirements, even on the demographic department, the question is how likely is it really for such a big region from Thrace to Punjab to stay that cohesive?
Depends on what part of Pakistan you're talking about I suppose. The Indus is a traditional border of the Iranian cultural realm, and you could argue that the Pashtun and Baloch regions of Pakistan would certainly count. Perhaps not Punjab, Sindh, or Baltistan though.
If we want more people (China after all didn't surpass 600 million until modern times) and an expansion of the Persian realm, there is always the remote possibility of Persian Siberia. Northern Kazakhstan has the upper reaches of the Ob-Irtysh system, and of course the Volga Delta in the north Caspian. I don't know how much an Early Modern country could reasonably control of that region, though--maybe just the majority of the Ob-Irtysh watershed (to the Arctic), or maybe as far as the Sea of Okhotsk like the Russians. Their capital would probably be somewhere in Khwarezm or Khorasan, and the rulers perhaps akin to the Seljuks or the rulers of Khwarazm. Persian settlers or deportations from the already vast Persian Empire (if the borders are like the Sassanids or Achaemenids at their height) could be used as frontier settlers.
But you still face the challenge of why a reasonable Persian ruler should conquer and subdue Central Asia (mostly poor) and Siberia (even poorer) when they could instead go for the real prize--India.