Can I qualify for a Federal job,CDC or V.A. Hospital if I have a felony(1 year probation). M.A degree.?

I would like to know if I'm wasting my time seeking State or Federal jobs. I recently worked for 5 months at The USAF Judge Advocate Generals Office thru WRP sponsored by the Department of Labor for disabled college students. I received an excellent reference and Certificate from the Judge Advocate. My disability service connected rating is 50%. I'm currently pursuing a Curriculum & Instruction Ed.S which I'm hoping will allow me to become an instructor at a college or university. I researched the moral character statement for the OPM; it doesn’t specifically address disqualification for a felony. Is someone with knowledge of federal hiring guidelines or rules for Georgia State government and education jobs out there? I've spent years repairing my character and moral comp by volunteering for Covenant Hospice for three years and providing free Media & Video Instruction to at risk youth. I currently hold a B.A. Media, MA Health Care, Certificate: Health Care Ethics. Please help.