Financial security is the top priority of most households. When finances are not stable, families tend to hoard what little cash is available to them. When deposit insurance is available, families feel better about allowing the budgets to bend and flow along with the economy. With deposit insurance, depositors feel more secure about their money being there when needed.
I think they are way overdue for deposit insurance and I think they are risking a run on the banks if their economic down turn continues, but I don't think starting deposit insurance will do anything to actually stimulate the economy in any real and meaningful way although it can't hurt.
Deposit insurance is typically a government backed scheme whereby depositor's savings are guaranteed, by the government, up to a certain amount in the event of bank or other financial institution failure. Whilst the introduction of a scheme of deposit insurance in China would most likely reassure depositors that their savings are secure, it is difficult to see how encouraging people to save money, as opposed to spending money, would stimulate China's economy. Economic stimulus is generally built on investment and spending to generate growth, not saving.
I think China had it right when they attempted to institute communism, although they actually never successfully did it. The more they adapt to capitalism and sacrifice the ideals of equality, the worse they are going to get. Deposit insurance, which is a way for the government to encourage the use of banks by increasing their perceived safety, will just make things worse. Banks are not good for people - they charge fees and encourage overspending and create more economic problems. China should go back to the pure Marxist ideals of distributing wealth evenly amongst all citizens. That is the best way for China to improve its economy.