Can you throw diseased plants in a wet anaerobic compost bucket?

Normally you burn diseased plants.  The problem is that fungus, bacteria and viruses once spread into an orchard or larger area are impossible to control.  So, if you replant with a vulnerable species, eventually that plant will get the disease.  That is why you should only plant varieties that are resistant to disease.  Why there are root stock and grafted trees, etc.  Cotton root rot is a soil fungus that is dormant in old cotton fields, which is where ever cotton will grow.  You can put a vulnerable plant in the ground a 100 years later and it might die from the fungus.  So, to answer your question.  It really doesn't make much difference because whatever killed the plant is still there.

Every year, I have the same tomato disease. (blight) It over-winters here in the midwest USA and comes back again.

Not a good idea. THEORETICALLY, the heat of composting should kill the pathogens but that doesn't always happen.