No.
You need a Kor Ror 11 (I think, going off memory), which is a legal document from the courts or your local amphur signed by your wife in person that you are the legal guardian of the child, not her. Even then, if you are married, the IO will likely refuse and insist that you must extend based on marriage.
There is a similar situation where a foreign father is married but the Thai wife and mother works overseas, living him in Thailand living with their son. Immigration don't give a marriage extension because the wife doesn't even live in Thailand, never mind with them, and they are married so they refuse to extend based on parentage and insist it must be based on marriage because he is married to the Thai mother.
They don't want loopholes for foreign husbands to not have to keep 400k in the bank for months, so insist on marriage extensions for such situations.