It shouldn't matter. If BHO Sr is the acknowledged father, then BHO Jr was not born of two citizen parents. OTOH, if Frank Davis or Malcom X or some black sailor was the father.. and the birth certificate reflects that, or doesn't show a father at all, then Junior is an NBC. But unless it shows a name other than Barack Hussien Obama II, that would seem unlikely.
Two citizen parents on US soil is certainly the well-documented primary definition of NBC that I favor as well, but what is the intent of that language if not primarily to exclude foreign sovereign influence, as John Jay wrote to Washington?
If BHO II was a confirmed legal dual US citizen and subject of the Queen at birth, I am confident that SCOTUS would rule him to NOT be an NBC at least on a 5-4 decision.
I am not confident that they would apply that ruling retroactively to Obama, but the intent of the founders seems clear that they did not want, at a minimum, the foreign influence of claims of a foreign sovereign on the POTUS as would be the case if Obama was legitimate UK subject at birth as well.
I don't think I can say with confidence how SCOTUS would rule if SADO was legally single and BHO II only had a unitary US citizenship through his mother and NO claim of a foreign sovereign on him because of bigamy.
With an illegitimate father, any foreign influence would only be a weak influence from his illegitimate father and not a sovereign influence under the 1948 BNA. Such an illegitimate foreign influence would not be legally enforceable in any way by the father or the UK.
This makes for a much weaker case than if his parents were married and he was actually governed by the BNA of 1948 at birth. So to me it clearly does matter whether his parents were legally married in a non-bigamous marriage.
If Obama was born in Kenya, nearly all but the most die-hard Obamabots would agree that he is not NBC, which is why I believe he is blocking access to the likely evidential foundation of such a case against him, that being his HI vital records.