English dictionary defines trauma as:
An emotional wound leading to psychological injury.
So I'll say YES and NO.
YES in the sense that from the definition of trauma, there's emotion. Which means in oder to experience trauma after being cheated in a relationship there must be an emotional attachment. Which will not just cause trauma alone but also a possibility of psychological injury to the persons involved.
NO also if there's no emotional attachment in that relationship. It is usually called NO STRING ATTACHED. Yea, there are relationships like that or should I say FRIENDS WITH BENEFIT. Trust me, its still a relationship. Just that there ain't much responsibility or big deal, just for the fun.
So when cheating or even break up happens it doesn't affect much to the extent of causing trauma. Though there might be little or no concern from one party.
I hope this answer helps.