Would it be possible for a patient initially diagnosed with vascular dementia to be treated homeopathically?

Yes: The best way to treat and dementia is without pharmaceuticals. They don't work and the side effects are far worse than any benefit that can be achieved. Behavioral methods are best, combined with good nutrition and vitamin supplementation. Make sure the thyroid is working properly and there are no b vitamin deficiencies.

Would NOT risk it: Vascular dementia arises from strokes, and since risk of large stroke could be deadly, would choose a stroke specialist to prevent future events. Am unaware of any homeopathic remedy which could supplant standard medical prevention in this category.