Assuming for the sake of argument that she didn't file a claim, failure to have the claim adjudicated does not cut off the claim. The claim comes into being and dies based on facts, and those facts can be adjudicated at any time in a person's life. CRBA via the state Department is the typical and preferred route up to the age of majority; Certificate of Citizenship (N-600) afterwards, with application going through USCIS (INS). If the claim is denied, the applicant has recourse through the courts. There are literally thousands of cases of persons born abroad of one citizen parent, who have claims adjudicated. Quite a few of those make it into the court system.
There are some interesting historical cases, and assuming Cruz meets all the statutory requirements, his citizenship would be recognized at least for purposes of holding his Senate office.
Boyd v. Nebraska ex Rel. Thayer, 143 U.S. 135 (1892)
Elected governor of Nebraska, born in the US of an immigrant, the citizenship (not NBC, just plain citizenship) of the elected governor was challenged.
While there are definitely similarities, there are also differences rendering this case to not be a precedent for Ted Cruz's situation. For the question now becomes did his mother exercise her rights as a citizen before Ted attained majority? Did Ted's mother ever renounce her citizenship in either England or Canada? Until these questions can be determined Ted Cruz's citizenship remains in question. Also the fact that Ted Cruz held a Canadian citizenship up until 2014 would still require proof that somewhere along the line she was in fact eligible to confer her citizenship to Ted.
Bottom line, all of these questions guarantee he is not a natural born citizen, and questions remain as to whether he is in fact even an American citizen.