Personally, i dont believe it needs to be claimed but i dont know what your circumstances are. My understanding about CSA is that it does not affect your CL payments but i could be wrong of course. All i know is that our family tax benefit is not affected by my CSA payments. However im not on parenting payment so perhaps if you are getting that payment, it may be. You really need to ring and ask CL for clarification on that.
your ftb entitlement is based on what child support you are receiving. if you receive cash child support payments that you do not declare, you are being over paid ftb. if someone decides to do a tip off against you, you may have to pay back as much as 50c for every dollar you've been paid as cash. it's ALWAYS best to be upfront about payments you receive. all it takes is a small snag in your amicable relationship, him getting narky and letting them know what he's paid you as cash above assessment and you may have to pay a lot of money back to c'link