Are you working forward in time from his baptism, or back from a descendant whose details you are more certain about? In other words, do you know anything else about the Francis Hogan born some time before 1852 in 1839 (presumably in Ireland)? For example did he turn up in any later civilian censuses along with his family and did he marry?
Was it a Catholic baptism? If it was then I think it less likely that his birth and baptism would be separated by more than a few weeks or months, since his mortal soul would have been in jeopardy during that time, and one assumes his parents were good Catholics so they believed the Church's doctrine on this matter, as they did get him baptised.
I think you could be following a false trial if you have only a single mention of army service for someone with the same name, and trying to make that fit 'your' Francis. Clearly if he was the soldier in the Second Battalion of the 20th Foot in 1861, he can't have been born in about 1850/51, as the Army didn't recruit ten year olds. However if a later census gives his date of birth more accurately than his baptism record appears to indicate, and it says he was a former soldier or an army pensioner, it would clearly make it worthwhile to try and find his service or pension record.
Afternote: Sorry, failed to read the title carefully enough! That's a very big gap between his birth and his baptism. My basic point about not trying to work back from the 1861 Army census, without any other corroboration that he may have been in the Army, still stands.
