In many ancient Mesopotamian societies beards were a sign of masculinity and health; and literary evidence shows us how important and widespread beards were to cultures at the time.

one Assyrian medical tablet states that "if the hair on a persons cheek falls out a lot, the gods and goddesses are angry with that person"^[1] and in Akkadian culture growing a beard was a integral component of become a etlu or "young man".

So based on the literature I would say the beards were very much real; Regardless, the only known tradition of false beards anywhere in the Near East is in Egypt.

As for how the beards were managed and groomed; I don't know of any conclusive answer, but the main theory is that they used hot tongs and waxes to artificially curl the beards; in addition to dyes and jewelry embedded into them^[2]

[1] Harris, Rivkah. Gender and Aging in Mesopotamia: The Gilgamesh Epic and Other Ancient Literature. Norman: U of Oklahoma, 2000. Print.

[2] Wilcox, R. Turner. The Mode in Hats and Headdress: A Historical Survey with 198 Plates. Mineola, NY: Dover, 2008. Print.