It is partly accurate, but mostly inaccurate. There are many sources that prove Persian women were extremely good with makeup, but about the men, there were fewer primary and secondary sources that I could find. Hopefully, someone would be able to provide them. A lot of sites mention eyeliner in the Egyptian manner and that Darius the Great and Soranus wore makeup, but didn't provide good sourcing. Anyway, they surely cared about their appearance, as the men having well-groomed long hair and wearing jewelry is well documented and visible in statues and artifacts of the era.

However, the way you phrased your question seemed biased, as it is extremely close to "were they effeminate" which they were absolutely not. They wore thick beards and were trained soldiers, so the way a leader of the Persian army looked was more muscular than skinny. The Immortals were the Emperor's guard and also a standing army, and they always trained heavily and prepared for battle, being recognized as a remarkable force. Just look at the statues and artifacts again. If you want to picture their built a bit better in terms of recent media, think Khal Drogo.

Hope it helped.