The 1877 baptism is an adult baptism of the older Joseph Henry Adams
30th May 1877 St James Hampstead born 25th October 1842
Joseph Henry Adams parents James Ellis and Ulissa
20 George Street, no father's occupation given
Next entry same day born 4th October 1846
Ann Adams parents Eli and Elizabeth, 20 George Street, no father's occupation given
This now makes the only relevant death I could find make sense:
Ulissa Adams, age 80, Holborn, 1889 (born c1809)
i.e. that makes sense for the mother of someone born 1842, not the mother of someone born 1877.
Pursuing my Royal Marines theory ... I'm wondering whether Marguerite might actually not have been French.
First, there's good info to support the Irish possibility -- in the 1901 Irish census, there is no Marguerite (or variation) Strain specifically, but there are a load of Margarets and Maggies, for example, and loads of Strains generally.
But back to the Royal Marines ... they were based in Lympstone, Devon, between Exeter and Exmouth. (There is also a Sgt J H Adams shown on the Royal Marines Medal Roll 1914-1920 at findmypast.)
After Ivy's birth, French-born Marguerite SATRIN was a governess in Ideford, Devon, nearby. She died unmarried in Maidstone in 1959 at age 79. (Satrin is a very uncommon name in France: only 3 births 1891-1915, the earliest that geopatronym.com shows.)
Child of unmarried parents, fostered out and told her mother was deceased? A bit far-fetched, but sometimes truth is stranger than fiction.
But "born in France" is a not-uncommon tale to cover a multitude of ... things. My gr-grfather's sister's descendants were told that about their ancestor, the sister; I've worked on the odd such tale on forums like this. Quite often (and I suspect in my gr-grfather's sister's case), it really meant born on the wrong side of the blanket, rather than the other side of the Channel.
It's too bad we have no idea who the brothers were or how a stepmother came into the picture. Here's another theory, though, that would go with a Royal Marine who was absent and did take responsibility for his daughter to whose mother he was not married.
December quarter 1911 in Willesden:
a Joseph H Adams married Florence E Naptin
She was Florence Emily Naptin; parents Thomas George Naptin and Louisa Mitchell married in 1903 although they were together in 1901. (In 1901, Florence's age is mistranscribed at Ancestry as 1 rather than 10.) Ah, here we are: birth registered as Neptune, as they are shown in 1891.
Anyway, the Adams-Naptin births are:
Sept quarter 1911 (i.e. pre-marriage)
Elsie L E, Willesden 3a 563
George E H, Willesden 3a 522
... odd, as they would have to be twins
Sept quarter 1913
Violet E, Kensington
Sep 1916
Iris D, Paddington (mother shown as Napton)
Sept quarter 1918
Irene J, Paddington
-- could be a posthumous birth if father died late 1917
Dec quarter 1920
Edward R, Paddington
-- died 1923 Paddington
-- could be a birth to the widow ...
In any event, this appears to be the story of the Joseph H Adams who married in 1911. There isn't really another London-area marriage for the name Joseph H(enry) Adams from 1900 onward, early enough for there to be children by 1917, except one in Stepney in 1900. But what it would seem to indicate, for this one, is that there was only one brother in 1917 in that family, whoever they were.
These locations are also consistent with the Kilburn place of birth for the Royal Marine. And not far off the location of the death registered in early 1918, Marylebone, which resembles the Royal Marine by birthdate -- who of course is not necessarily our JHA any more than any others are. Our JHA could have had sons born before 1911.
But when investigating a "possible", I tend to try to follow them to the bitter end!
Question -- did Marguerite herself register the birth? (If she had died in childbirth or been incapacitated and then died, a third party would have registered it. It can just help to know for sure. I'm thinking, if she did die not long after the birth, and if the names are all true of course, it could be that JHA would have married her had he not been serving overseas when the pregnancy became known and the child was born, and didn't have a chance to do that because she died.)