I have a Basil plant that appears to be affected by Fusarium wilt. Let's assume my diagnosis of the plant's issue is correct. Can I safely harvest the whole plant and eat the leaves that haven't wilted yet? Does the fungus that causes Fusarium wilt affect humans at all? Sources are preferred.
What you have on your basil is a strain of Fusarium oxysporum, obviously a strain pathogenic to plants.
Apparently, other strains of F. oxysporum can cause onychomycosis (nail infections) and keratomycosis (corneal infections). And if you have a very low neutrophils count, it can cause aggressive infections throughout the entire body and bloodstream.
Because these are different strains, you should be fine eating the basil, I've done it and suffered no ill effects, although it can alter the flavor. The plant strain of the species would have to mutate in order to affect humans, because the food source is drastically different, and a fungus that is adapted to one source will die if introduced to the other as a food source. The metabolization process is very different.
In other words, be aware that there are some human pathogens in the species, but what you have isn't going to hurt you, unless you have an allergic reaction to the fungus (unlikely but possible), which I suppose you could test (by consuming a small quantity first) if you have known allergies to other fungi (such as penicillin, button mushrooms, etc).
Here is a good paper on Fusarium Pathogenomics.