Yes, it does if no treatment is taken. The main two diseases that have an increased risk after menopause are the bone weakening condition; osteoporosis, and cardiovascular disease, which includes any disease of the heart and blood vessels such as heart attack and stroke. Taking HRT can reduce the risk of both developing in later life.
There are other diseases that increase after menopause and relate to a lack of hormones such as type 2 diabetes, depression, and dementia and although evidence is still emerging, some studies suggest that HRT can have a beneficial effect on these risks too.