I think it is, I found this family tree in Google:
http://familytreemaker.genealogy.com/users/s/h/o/Andrew-D-Shore/WEBSITE-0001/UHP-0159.html
which shows that his dad was having illegitimate children with his servant too (before marrying her).
This website shows
Children of William McCulloch and Margaret Steele are:
David McCulloch, b. 1864, Wishaw, Lanarkshire, Scotland, d. 27 Apr 1877, Cumnock, Ayrshire,
+Thomas Steele McCulloch, b. 21 May 1867, Wishaw, Lanarkshire, Scotland, d. 16 Mar 1930, Auchinleck, Ayrshire
William McCulloch, b. 04 Jan 1869, Riccarton, Ayrshire, Scotland, d. 24 Aug 1890, Linkieburn House, Muirkirk, Ayrshire
Jessie McCulloch, b. Feb 1871, Riccarton, Ayrshire, Scotland, d. 10 Mar 1871, Riccarton, Ayrshire, Scotland.
+John McCulloch, b. 10 Jul 1872, Kilmarnock, Ayrshire, Scotland, d. 10 Feb 1943, Old Cumnock, Ayrshire,
Helen Watt McCulloch, b. 16 Oct 1874, Dreghorn, Ayrshire, Scotland, d. 25 Jun 1936, Kelvingrove, Glasgow
Jessie Watson McCulloch, b. 11 May 1876, Dreghorn, Ayrshire, Scotland, d. 21 Mar 1947, Partick, Glasgow
David McCulloch, b. 14 Dec 1878, Linkieburn House, Muirkirk, Ayrshire d. date unknown.
No mention of Jessie Sloss

. If our presumptions are correct, these will be William McCulloch Sloss' half siblings.
Perhaps, John, you could get in touch with the tree owner. Not only may you get some evidential documentation about William McCulloch your 'alleged' great grandfather, you may also be able to surprise them with the knowledge of Jessie & her offspring!
Josey