Current recycling tech is pretty terrific (IIRC ~98% recovery of lithium, misc metals). Enabling the long fabled "circular" economy.
At some point we'll hit a (near) equilibrium. IIRC, ~20 years out. (Assuming Li-ion battery tech continues to improve at current rate. Thereby balancing out the lithium lost during recycling.) So we'll hit something like "peak lithium", greatly reducing mining (extraction) of new lithium.
Recycling is much cheaper than mining (both $ and CO2).
(I believe, but obliviously can't prove, that sodium (et al) batteries will enable new use cases and markets, complimenting lithium rather than replacing it.)
In any practical sense, no, it's not. Its a dumb argument pushed by people trying to sandbag EVs.