Maybe this question would be better phrased, does Parallels fall into the category of software that runs poorly on the new M1 chipset?
It does for most use cases where you want to run images meant for different CPU architectures, like amd64. It shouldn't if you want to run something meant for the same CPU architecture, which isn't going to be a thing for a long long time.
Why not? If you consider there are 3 main desktop OSes, these are Windows, macOS, and Linux. MacOS and Linux already work on ARM64.
For Windows software, CrossOver for Mac runs on M1.