Will a bad water pump stop fan clutch from engaging

I believe your fan clutch is an "electro-viscous" type - meaning an electrical signal due from the engine processor influences clutch engagement. This would mean that diagnostic testing of engine performance and cooling system operation is needed to figure out why the clutch will not work properly. Keep in mind you didn't share which engine you had, so I'm making an educated guess. I do not see how a water pump being "bad" (bad - how?) could cause a fan clutch to not work properly. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops