Yes, logic capability is available.
Please have a look at my previous example thread for KiCad6 at Simulation examples for KiCad/Eeschema/ngspice - #4 by holger. You have to scroll up a lot, then you will find an example for a (fast!) digital simulation.
The project is now also available at More simulation examples for KiCad/Eeschema/ngspice, ready for 8 (see next post).