You cannot say NO and then say it is NO only for the average Joe. 
The answer should be ...YES, but you have to apply strict measures to be 100% anonymous. You are also looking at this from the angle of someone hosting a node and not the average Joe that learnt how to make a secure Paper wallet. 
Throw Paper wallets and Mixers together and you have a better chance to stay anonymous... until you use those bitcoins at a regulated exchange or a third party service where your real identity is linked to your payment or delivery of goods.
It definitely isn't absolutely impossible but it is in a sense still fairly hard to ensure 100% anonymity. Bitcoin in the first place is not designed around the concept of anonymity but rather to enhance anonymity. The answer should be ...YES, but you have to apply strict measures to be 100% anonymous. You are also looking at this from the angle of someone hosting a node and not the average Joe that learnt how to make a secure Paper wallet. Throw Paper wallets and Mixers together and you have a better chance to stay anonymous... until you use those bitcoins at a regulated exchange or a third party service where your real identity is linked to your payment or delivery of goods.
Sure, moving coins around mixers would help your cause but it doesn't mean chain analysis isn't totally out of the picture, the mixer won't go rogue and reveal your origin and destination addresses. There are just too many points of failure as compared to the cryptos that were specifically designed to focus on privacy. Unfortunately, no matter how much one values its privacy, Bitcoin is probably not the best crypto for the job.