I'll make the argument: No, instructors should not use this tool at Chegg.
In general, Chegg is among the worst actors of the online academic community. Their business model is fundamentally predicated on supporting violations of academic integrity, fraud, and malfeasance. In this sense, we should not be supporting them with engagement, mind-share, or test cases for their systems.
In the same vein of general lack-of-trust, Chegg is not an entity that can be trusted with our exam information. Despite the fact that they currently claim no IP rights to uploaded exams, and a promise to delete information after a month, their promises are not reliable, and we should not give them an opportunity to use our exam information in any scurrilous fashion in the future.
Additionally, the details say that attempts to post such exam questions to Chegg are simply blocked, with no record of such attempts made. (Per website, "We will not be able to provide any information regarding users who attempt to post a blocked Exam question during the Exam Timeframe.") This short-circuits the possibility of detecting students who make such attempts, and giving required corrections to the students in question. Students may also invisibly be driven to some other platform or method of cheating at that in those cases.