(I am not a health professional, this should not be counted as medical advice)
I am not going to lie: vegetables are important for a vegan diet, or really, any diet. You may be able to eliminate them, but you may have to take supplements. This is true even if you aren’t vegan and don’t eat veggies. Veggie-less vegans have to be more careful about their nutrition, but it is possible. Some previously veggie hating vegans have found they were able to get over their aversion, some grind them up into smoothies or sauces to disguise the taste. Some simply take veggies in capsule form. Some even get their nutrients elsewhere. It may involve eating more faux meats than veggie lovers.
If you are worried about losing the taste of wonderful food, fear not, lots of vegan recipes do not require veggies, or at least not veggies you can taste.
If you need expert advice on nutrition, I recommend contacting the Physician’s Committee for Responsible Medicine, http://www.pcrm.org