Can one travel Australia to Haikou VIA SHENZHEN and get a VOA in Haikou?

This is possible only with pre-arranged Chinese visa and in this case you would not need Hainan VOA. The problem with this itinerary is your flight to Haikou via another mainland China airport. In case that you want to aplly for Hainan VOA or even better for Hainan 30-Day Visa-Free Access you have to fly from an airport located outside mainland China. Also, when we talk about Hainan 30-Day Visa-Free Access it is important to mention that you do not have to travel to a third country, i.e. it is just fine to travel, fore example, Hong Kong - Haikou - Hong Kong.