Is it okay to apply for Medicare-Aid coverage while starting application process for Veterans Aid and Assistance?

Dad had Medicaid coverage of his Medicare insurance premiums in his previous home state(Medicare-Aid) as well as medical coverage after $700 spend down/month(with less than $900/month SSI). His housing-related costs alone ate up his income in the winter months. I moved him to live with me in NC and got him signed up for medical care through the VA. He lost his Medicare-Aid coverage when leaving his home state. I've learned about VA A&A, and understand he'd not likely qualify for Medicaid once he has Aid and Assistance coverage. He could use the extra $100+/month Medicare-Aid coverage while waiting the 1 year or more I hear it takes for VA A&A. He has significant debt to pay back as well as ongoing personal expenses so anything extra would help.