The answer to the above question is straight no. Mining Bitcoin providing you a service and you are getting the value as a return for mining which is not the situation with Ponzi Scheme.
Let\'s start with the explanation what is Ponzi Scheme. It is a fraud which creator is Charles Ponzi. In the one of the novels by Charles Dickens, similar scheme was described so there is some presumptions that Ponzi got the idea from novel. Ponzi Scheme is working with attracting investor through the great profit, paying them revenue gained by newer investors.
Ponzi Scheme is not doing any activity or business that are making profit. It worked through attracting new investors and it is judged to fail it is just matter of time. There are some possible ways how these kind of fraud is stopped, or the authorities stop the fraud, or the organizers (investors) run away with money. Even if no one stop the scam it will not last long because further progress requires more resources and investors, and at the some point investments stopped. Ponzi scheme will not last more then ten years. Bitcoin market survived global economy crisis and some kind of crashes several times.
Anyway, the concept of Bitcoin mining is completely different, it is based on computational power. The biggest differ between Ponzi Scheme and the Bitcoin is that there is a real service and real profit in the mining. People that are mining or miners are sharing their hardware to the network and gets Bitcoin or any other coin that they are mining in the return. Computational power is the foundation of the network. It is used for solving mathematical problems and for making transactions too.
In the text above we highlighted the differs between Ponzi Scheme and the Bitcoin mining. The most important differ is existence of actual service, actual profit, actual activity - mining.