Yes, it will work on new M1- at least on the most current version of Lightroom Classic as of writing this (v10.1). This version of Lightroom Classic is still using Rosetta 2, so nothing has really changed for Lightroom Classic at the moment for M1 users.
When Lightroom Classic is updated to work “natively” on M1 chips, it wouldn’t surprise me if there were some “kinks” to work out to make sure everything is still working with plugins.
So I would recommend turning OFF any kind of “automatic updates” from Creative Cloud, and when Adobe does release an M1 native version of Lightroom Classic, you may want to hold off upgrading for a bit while the kinks are worked out.
I personally don’t have an M1 machine, but I’ve had at least 3 users confirm that it is working fine on M1 + Lightroom Classic, and I wouldn’t expect otherwise because Lightroom Classic is still using Rosetta 2.