Can you accept him as your son even if he isn't the next Count Vorkosigan?

Dhirender who initially refuses to see the child but accepts the baby as his own son.

He accepted him as his beloved son, and asked him to render assistance in battle when required.

Why could they not just accept me as Vorna's son?

She had first accepted Kabir whole heartedly as her son.

"Do you think you will accept him as your son someday?"

He finally accepts him as his son and promises to live together, and they leave the plains to find their new home.

Perhaps on some subconscious level she accepts him as her son, regardless of his birth.

How could a lord accept that kind of man as his son?

Since her first steps, she'd adored the man her father had accepted as his own son.