Not likely to kill battery as JFP notes but possible.
I have had both a Ctek and a Battery Tender Jr. go bad on me. Rare but happens. CTek unit just stopped working - it was ~ 15+ years old so didn't really "owe" me anything. The BTJ (maybe a year old) would work for 2-3 minutes (I found out later after working flawlessly prior) and then go into fault. Subsequently did a great job draining a 1yr old AGM battery. Costco refunded the BTJ and helped cover cost of new power plant - battery was perfectly fine before but obviously compromised w who knows what discharge caused by BTJ.
Simple test would be to put Ctek unit onto another vehicle and see what happens and go from there.
Good luck
