Verdict: No, dangerous
Walnuts are dangerous for dogs. While the nuts themselves can cause gastrointestinal upset and obstruction, the primary concern is black walnuts (Juglans nigra) which contain juglone, and all walnuts are susceptible to developing tremorgenic mycotoxins from mold, which can cause severe neurological symptoms.
Juglone can cause gastrointestinal irritation. Tremorgenic mycotoxins interfere with neurotransmission, leading to neurological dysfunction.
Juglone (in black walnuts), Tremorgenic mycotoxins (from mold)