Sure why not
Can black black men dye their hair honey blonde in the USA army?
I don't believe it is forbidden, but a soldier's superiors can decide if an artificial hair color is out of compliance. "It is the responsibility of leaders to use good judgment in determining if applied colors are acceptable, based upon the overall effect on a Soldier's appearance."
It is not expressly forbidden however there are rules pertaining to bringing undue attention to oneself while in uniform, If it causes a major distraction or ridicule it will be forbinden.
Extreme, eccentric, or trendy haircuts or hairstyles are not authorized. If soldiers used dies, tints or bleaches they must choose those that result in natural hair colors. Colors that distract from professional military appearances are prohibited. Soldier should avoid using colors that resulted in extreme appearance..... And that's a fact Jack!!! :)