Can a person who receives a Bad Conduct discharge be considered a veteran of the armed services?

SSG Gordon Hill Here are two references:

What is a Veteran? The Legal Definition
What is a Veteran? Title 38 of the Code of Federal Regulations defines a veteran as “a person who served in the active military, naval, or air service and who was discharged or released under conditions other than dishonorable.” This definition explains that any individual that completed a service for any branch of armed forces classifies as a veteran as long as they were not dishonorably discharged. However, with regard to applicable benefits, other considerations are important and will be covered in later sections.

https://www.thebalancecareers.com/what-is-a-veteran-3976315

My younger brother got a BCD, with prison time. When Carter pardoned all the dodgers that went to Canada, he tried to have it upgraded saying he deserted for the same reasons as the draft dodgers. No luck, but he never considered himself a veteran.

No.