The simple answer is yes, but with certain conditions!
Challenge coins have always existed outside the traditional rank and honor system and as such no special authority is required to make, own, or carry a coin; however you must do so with the weight and knowledge of what challenge coins represent.
What's crucial above all else is to grasp the history, traditions, and etiquette that come along the decision to become a coin carrier. Coins represent trials and tribulations in nearly all that carry them and no matter the artwork adorned upon them, choosing to carry a coin should be done with a backing of respect for what that coin represents.
Zach's rules on Coin Ownership:
Coins should be earned, but may be bought for oneself as a representation of accomplishment or the path towards it;
Coins should be carried at all times and to have an empty pocket should be to feel a piece of your soul to missing;
Coins should represent something to you and should act as a permanent reminder of whatever that is;
Coins should be shown, talked about, slammed on bars, cherished, worn down, scratched, tarnished, and ultimately, loved;
When invited, a civilian coin may be presented during a coin check, however the carrier of the civilian coin should still buy the carrier(s) of the military coin drinks, not out of defeat, but rather out of gratitude;
A person presenting a coin of perfect condition, without scratches and other signs of wear, should be treated the same as person wearing new or overly clean Carhartt pants; with distrust and skepticism until proven otherwise;
and finally, coins should be given freely and accepted graciously!