Are there consequences if a parent who is a Dependent receives health and pension benefits from the military?

I would contact the nearest service organization such as the VFW for information.
I have never heard of money being involved in declaring a parent a dependent. Dependent status usually involves only privileges of on base services, such as exchange, commissary, movie theaters, etc. If you are looking for tax status, that would be a whole nuther story. The pass and ID office would be able to answer this a little better.
As for medical care I doubt the parent would qualify but since the services do billing now, the parent may be able to use the base facilities and medicare would be billed. But if the parent has a civilian Dr. I would encourage the LO to use that Dr. since the Military usually transfer every two years so little continuity of service. Medicare would be first payer for services and if the LO should be eligible for tricare, that would be second payer.
Remember that the gates are manned by armed security personnel and anyone entering needs to be cleared and the dependents ID would be cleared for entry.

LMP - my answer above assumed that you were claiming your parent as a dependent for tax purposes. Health benefits from the military - I have no idea what the criteria for that are.

It won't affect the pension, but I don't see how you can claim the parent as a dependent since the parent has taxable income above the income limit ($4,050 for 2017).