If a man eats very little vegtables can that cause bad health?

Probably not. In one natural experiment, the gauchos of argentina in the mid-1900's ate nothing but meat and seemed none the worse for it. This may not be a popular answer, and i'd encourage you to vary your diet sensibly. The big concern is Folic Acid deficiency, but less so since food nowadays is fortified to meet the needs of most folks.