On the principle that names on baptism can sometimes change from the registered name, there is a birth registered in Warwick registration district in the right quarter for the baptism.
From FreeBMD
Births Sep 1906
Marks Muriel Alice Warwick 6d 696
However there are three other Marks births registered in Warwick 1901-1908 so I wouldn't say I find it compelling evidence.
The 1901 census does show Mercy's sister Rose (as in Mercy born Walsall) as a servant in Leamington
RG13 2932 folio 166
30 Leam Terrace Leamington Priors Warwickshire
Rose Marks 17 Walsall, Staffordshire, General Servant Domestic
as well as two other sisters
RG13 2932 folio 142
Bowling Green Inn 18 & 20 New Street Leamington Priors Warwickshire
Charles Duffin 38 Old Stratford, Warwickshire, Head Married Beer retailer
Catherine Duffin 34 Princees End, Staffordshire, Wife Married
Hilda Duffin 7 Leamington, Warwickshire, Daughter
Kathleen Duffin 2 Leamington, Warwickshire, Daughter
Frederick Duffin 4mths Leamington, Warwickshire, Son
Hannah Markes 20 Walsall, Staffordshire, Sister-in-law Barmaid
Marriages Dec 1892
Duffin Charles Walsall 6b 1145
Markes Catherine Walsall 6b 1145
I think Mercy's mother's maiden may have been Morgan
1871 census RG10 3006 folio 148
30 Albert Street Sedgley Staffordshire
William Morgan 50 Willington, Shropshire, Head Married labourer
Sarah Morgan 52 Tipton, Staffordshire, Wife Married
Thomas Morgan 21 Tipton, Staffordshire, Son Labourer
Harriet Morgan 17 Sedgley, Staffordshire, Daughter
Joseph Marks 8 Sedgley, Staffordshire, Grandson
Joseph was not with his parents and siblings on the 1871 census.
I suppose it could be possible that Day is Arthur's surname and Lawrence his middle name if he wished to disguise his name in anyway. However having searched that doesn't seem to throw up any further Arthur possibilities.
Regards
Valda