The baptism for Absolom say his mother is Ann Crook with no mention of a father. This would normally indicate that he was illegitimate.
I would think that the marriage at St Peter, Bolton, Lancashire in 1756 between Ann Mellen & Abraham Crook was unlikely to be the parents of Absalom. They were both widowed when they married and of the parish of Bolton, Lancashire. Do you have any evidence that they moved south.