Yes, you can use an HSA account at the VA hospital. This is a relatively new change in the rules and was put into place April of 2013. There are some restrictions on what you can pay for with your HSA funds.
According to the VA Consolidated Patient Account center website you can only use your HSA funds to pay your “VA first party copayment”.
As far as your High Deductible Health Plan(HDHP) goes, the VA will accept and bill these plans only for charges incurred for non-service connected disabilities.
Here are links to the VA’s HSA factsheet can be found here, and a link to the article talking about their authority to bill health plans.