According to this post, the answer is yes!

GitHub user @mwidjaja put up some notes on his GitHub repo. In there, the key takeaways I saw are:

1. It's complicated.
2. Homebrew doesn't work, unless done with x86 emulation.
3. To enable Rosetta to do x86 emulation all the time in a terminal, we follow instructions here.
4. Install miniconda for macOS ARM.

The conda-forge team has done a lot to port over the entire conda stack to Apple Silicon. See more here.

As of 21 November 2020, the conclusion I have is that "no, it's complicated, don't try running Anaconda on M1 macs just yet".

Rather, for data science use cases, a remote server is a better investment.