It does seem possible that COLLINS and COHEN are the same man. The circumstantial evidence is good.
One way to confirm would be to link the physical descriptions, if not by the tattoo, then by height, facial shape, eye and hair colour etc. Since your Samuel Collins was not a serious criminal, but rather a public nuisance, it is not surprising there is not a detailed description of him in police records.
The other way to confirm we have found the right man would be through DNA.
SUMMARY:
• Both Samuel COHEN and Samuel COLLINS are born about 1816 in London
• Both are Jews and both convicts
• Both can read and write
• Both travelled on ships “Mangles” and “William” (this is the most compelling fact)
• Both are in labouring-type/ unskilled occupations
• COLLINS said he had been in the colony from about 1835, which is the same year that convict Samuel COHEN arrived.
• There is no record of a convict named Samuel COLLINS of the right age arriving in the correct time period.
• Both men have records in Australia of “nuisance” and “disruptive behaviour”, but no particularly serious offences.
• COHEN arrived in Sydney from Tasmania in Oct 1845. I cannot find any evidence of a Samuel COHEN in Sydney after that date (no marriage, or death, or newspaper reference).
• Assumption - COHEN changed name to COLLINS between 1845 and (at the latest) 1855
Some general speculation:
• As you say the lack of a marriage may be due to his Jewish religion, or perhaps there was a church or synagogue marriage that does not appear in the formal registrations, as it occurred before this became compulsory.
• Samuel does not use any Cohen family names for his children. Had he felt abandoned by his Jewish family in London, he might have avoided their names, and perhaps was reason to change his own surname.