In common-law countries there is a legal maxim "de minimis non curat lex" (loosely: "the law will not involve itself in trivia"). So they could sue, but the court would reject it. This makes the morality question irrelevant.

Immediate edit: in the specific case here, where the IT contractor would indemnify the agency, this would be for disputes between the manufacturer and the agency. So the scenario LanX is proposing is that the manufacturer would threaten to sue the agency for the contractor's haircut. Let's not forget that if the contractor has an agreement with the agency, a court would still adjudicate it, and common-law courts don't favour things that would "bring the law into disrepute", which this surely would.