Yes, because it would cause no "red flags" whatsoever to invite CPS into your home, then when they ask a question you don't like or try to look somewhere you haven't approved of, to quickly usher them out of your house and insist they get a warrant
I just prefer to bypass that all together (because chances are they would ask a question I felt I didn't have to answer to want to look in a place I felt too personal) and actually exercise the rights I wish to keep.
I guess if you ever encounter that situation (and I wouldn't wish that on any loving, involved parent), you can feel free to roll the dice and allow someone to enter your home without cause or warrant, waiving your rights and allowing them to conduct an investigation with no checks and balances. That's totally your right, to waive your rights -- because even if they leave in 15 minutes and eventually "close the case", make no mistake that once they have entered your home they are conducting an investigation. If one is totally okay with one party having all the allowances while another party (you) have waived your rights... go for it, but I can tell you there is not one lawyer worth a roll of quarters who would advise someone agree to a search or interviews with children without a warrant... innocent or not.
I said in my other reply I don't know how CPS specifically is mandated in that regard, but with the police -- if you invite them into your home without a warrant, you cannot just "tell" them to leave and get one when you're done talkin'. You would then be "impeding an investigation" (or they could envoke that, rather) and they leave when they're good and ready. If you're 100% certain CPS isn't entitled to work within the same framework -- feel free to invite them in without a warrant, then tell them to leave if they (as you say) "cross the line" -- but by that time, they will have had enough evidence (because you've let them in then refused to cooperate, which makes no sense) to obtain a warrant.
If people would like to use the constitution as no more than toilet tissue, that's their business... I prefer to actually use the rights contained therein to my benefit, as intended when it was written.