No, a veteran or a disabled veteran cannot file for free or get a reduced rate. Only active military are eligible to file for free based on their eligibility as shown on this TurboTax website - https://turbotax.intuit.com/personal-taxes/online/military-edition.jsp
The online editions of TurboTax do have a Free edition that can be used. However, it is only for very simple tax returns that only requires a Form 1040 and no other form or schedule. If unable to use the Free edition based on the tax data needing to be entered then the Deluxe edition or higher would be required which are not free.