@ Ben. Yes it is possible to find work here with just a student visa but it is not legal. The last time I looked fines could be as much as 100,000 RMB plus a sum equal to illegal earnings. I know someone who as here on a family visa who got caught and fined. On his second offence he was imprisoned and subsequently repatriated.
As an illegal worker your employer may have guanxi but you don’t and an unscrupulous employer may even take advantage of your vulnerability knowing that you have no legal remedy to sue for breach of contract, failure to pay etc.
@ drjtrekker – the family visa, otherwise known as the residence permit, is designed to enable foreigners to visit China to be with their immediate (Chinese resident) family member(s) e.g. a spouse and/or children. It doesn’t cover fiancés and the tourist visa should be adequate for getting married. The family visa/residence permit is typically granted for a period of 3 years and is renewable providing that the holder hasn’t broken Chinese laws.