It's hard to believe that Dr. McCullough, even though this was not his field of expertise, would not have known this with all of his medical and biological training.
Nattokinase is rich in Vitamin K2 MK7, so I have no doubt it would boost the immune system (in conjunction with Vitamin D and Vitamin K2 MK4). Even early on the pandemic, it was proven that Covid patients low in Vitamin D and K2 fared much worse that those with robust levels.
I remember that quite clearly, especially about Vitamin D, and the discussions about increasing Vitamin K being a bit dicey because that is a coagulant would could worsen blood clotting if not very careful.
K2 is not a coagulant. K1 is instrumental in coagulation. Our bodies normally make K2 out of K1 (which is abundant in a normal healthy diet, even lettuce), but as we age our bodies are not as efficient at synthesizing K2, so we need to get it directly from diet (pastured eggs are a good source for K2 Mk4) or take supplements.
K2 is like the boss of where calcium goes. Low K2? It gets deposited inside our blood vessels. Boss K2 directs it to teeth and bones. In Japan, K2 + D is recommended for prevention of osteoporosis. K2 + D are also important for immune function.
Vitamin K2 (Menaquinone-7) supplementation does not affect vitamin K-dependent coagulation factors activity in healthy individuals
https://pubmed.ncbi.nlm.nih.gov/34115006/