Looking at the records, it is possible that John may have been brought up in Brighton, but not born there. The 1851 census for his elder siblings and IGI records suggest you should be looking at Hastings. Only his youngest sister Lucy appears to have been born in Brighton.
William, John, Maria & Ann all look to have been baptised in the Wesleyan Methodist Chapel in Hastings as the children of William Ade and Maria nee Cox.
The IGI records John's full name as John Wesley Ade, born 10th Feb 1832, baptised Hastings 11 March 1832.
The 1840 Brighton Street directory lists
BOOT AND SHOE MAKERS. Ade William, 27 George st, an address which would seem to tie in with the 1841 census
There also numerous shoemaking apprentice indentures under that name in the National Archives Index, several mentioning Brighton & Hastings.
The National Archives also state that on 1846 Sept, ADE John, 14, labourer of Brighton was sentenced to Transportation for 7yrs. Ref: QR/918 - 1846 Sept
Perhaps the local papers for September 1846 can tell you what his crime was.
Dont know whether Maria was a widow by 1841 but a William Ade died in Marylebone in that year and then some of the children turn up in that area in 1851.
Roy G