I actually think this is quite a difficult question the answer. The effect on the autonomic nervous system depends on the cause of the LVH. The most common causes of LVH are secondary to increased afterload, such as hypertension, aortic stenosis, rather than diseases of the heart muscle itself, such as hypertrophic cardiomyopathy.
In the case of increased afterload, there is reduced cardiac output, and so the baroreflex increases sympathetic outflow increasing heart rate and contractility, and also promotes LVH.
If the LVH is caused by something like hypertrophic cardiomyopathy, then as you have said, this may in theory increase parasympathetic outflow if the LVH increases cardiac output. However, the LVH and remodelling is pathological, and the LVH reduces the size of the LV chamber, which impairs filling, ultimately reducing stroke volume and cardiac output, which increases sympathetic outflow.