Absolutely, and not only in a strictly physical sense (i.e. it's contained within it). Mental acuity into old age is strengthened by continued exercise and fitness - damaging the body so that it is less able to physically operate damages the potential of the mind.

Even if you want to step into the realm of the philosophy of mind[1] - there still are rather clear portions of the mind that are physically linked and a pretty wide consensus on the feedback of bodily strength to a healthy mind. Modern dualism accepts that a lot of mental functions are either enabled or assisted by our physical brain goop and classical dualism still assumed the definition of some crossover point where the metaphysical abstract expression of thought was translated into physical signals that triggered actions in the body - the existence of pain reactions necessitates a fair amount of our mental processing having the direct involvement of physical systems.

1. https://en.wikipedia.org/wiki/Philosophy_of_mind

How could it possibly not be?

if the mind is a state of consciousness, and damage to the brain damages said consciousness, the mind must be part of the body.

going further, alcohol is interesting in that, in appropriate amounts, it can improve the state of consciousness through a better quality of social interactions, and at the same time, can damage the state of consciousness through poisoning

Yes, the mind is an emergent property of the networks of the brain.