- It shouldn't be possible for him to be denied entry, because logically, he is either a US citizen or he isn't. If he is a US citizen, he cannot be denied entry to the US no matter what, no matter what documents he has. If he is not a US citizen, there should be no problem for him entering on his UK passport and ESTA. So uncertainty regarding his US citizenship should not, in principle, prevent him from entering the US. However, is he even able to get an ESTA without lying about his US citizenship?
- Yes. His US citizenship is automatic and involuntary at birth according to US law, if the conditions for transmission of US citizenship to a child born abroad were met (which I assume they were or otherwise CRBA wouldn't have been an option). No action is necessary, and taking no action cannot make him not a US citizen.
Some additional information: This question has been asked many times on Travel.SE before, e.g. here. In the Foreign Affairs Manual, it is mentioned in 7 FAM 085(b) that it is permissible to issue a US visa to someone with a claim to US citizenship prior to a final determination of their US citizenship. By extension, it should also be permissible to enter on the Visa Waiver Program prior to a final determination of one's US citizenship. Immigration officers at the port of entry are not in a position to adjudicate the nuances of US citizenship claims (especially when it involves periods of physical presence of the parent, which often require extensive evidence of such periods of physical presence).