Maybe in 20 years. As usage of electric cars is still ramping up, demand for new batteries is going to outstrip supply of old batteries by far. And that's before we ask how difficult it is to extract raw materials from old batteries.
FWIW, my city (Lünen, Germany) has 2 Multi-MWh storages built from them (1 from batteries from Smart cars, 1 possibly from i-MiEV batteries). Without any material-level recycling, just simple reuse, as energy density is a lot less important than for cars.
Maybe having 2 of those (admittedly pilot) projects in my backyard biases my estimations of their availability.
FWIW, the majority of the EV fleet with air-cooled batteries in hotter US states (like Arizona) are already needing battery replacements after ~5 years. See LEAF and eGolf.