IIRC (two years ago...), I initially made a similar assumption, based on external evidence that did not suggest at all that this filiation might be real. But, of course, another possibility would be that Lichtenstein (who is only a secondary source here) had been misled to believe that Abdim was Muhammad Ali's son. He might write it, and mean it... but be wrong.
(If the birth dates out there are correct, they are also a bit problematic: Abdim/Abidin is assumed to be born around 1780, when Muhammad Ali (born in 1769) was still a boy. In the literature, Muhammad Ali's four elder sons are quite regularly given an explicit rank of birth: eldest = Ibrahim (born 1789; e.g. [
here]); second = Tuzun/Tusun/Tosun (born 1794; e.g. [
here]); third = Isma'il (born 1795; e.g. [
here]); fourth = Sa'id (born 1822; e.g. [
here]); this leaves no room for Abdim...)