God would be the God of the children of the saved parents, regardless if they take the sign of water baptism, as He will save those who are His elect still?
Yes and no...
In Gen 17 we see the result of rebellion:
11 And ye shall circumcise the flesh of your foreskin; and it shall be a token of the covenant betwixt me and you. 12 And he that is eight days old shall be circumcised among you, every man child in your generations, he that is born in the house, or bought with money of any stranger, which
is not of thy seed. 13 He that is born in thy house, and he that is bought with thy money, must needs be circumcised: and my covenant shall be in your flesh for an everlasting covenant. 14 And the uncircumcised man child whose flesh of his foreskin is not circumcised, that soul shall be cut off from his people; he hath broken my covenant.
The Holy Bible: King James Version, Electronic Edition of the 1900 Authorized Version. (Bellingham, WA: Logos Research Systems, Inc., 2009), Ge 17:10–14.
So, in the compound sense, yes, God would still be a God to the parent and child, but in the divided sense, they are cut off.
Consider the response of Zipporah to Moses:
Exodus 4:25
25 Then Zipporah took a sharp stone, and cut off the foreskin of her son, and cast
it at his feet, and said, Surely a bloody husband
art thou to me.
Poole writes:
"Perceiving the danger of her husband, and the cause of it, and her husband being disenabled from performing that work, whether by some stroke or sickness, or by the terror of so dismal and unexpected an apparition to him, and delays being highly dangerous, she thought it better to do it herself as well as she could, rather than put it off a moment longer; whether because the administration of that sacrament was not confined to any kind or order of persons, or because, if it was so, she did not apprehend it to be so, or because she thought this was the least of two evils, and that it was safer to commit a circumstantial error, than to continue in a substantial fault.
Matthew Poole,
Annotations upon the Holy Bible, vol. 1 (New York: Robert Carter and Brothers, 1853), 124–125.
"And because she durst not accuse God, the author of this work, she falls foul upon her husband as the occasion of it, and as a costly and bloody husband to her, whose endangered life she was forced to redeem with blood, even the blood of her little child, by which as he received a new life after a sort, so she did anew, and the second time, espouse him."
Matthew Poole,
Annotations upon the Holy Bible, vol. 1 (New York: Robert Carter and Brothers, 1853), 125.