No. It could be right without the comma, though I'd use 'whether'. "I doubt whether that is right in its true sense." The collocation is generally "in the true sense [of something]".
Some context would be necessary to say if "in its true sense" is right or not.
Or, depending on context, "I doubt that(1)that(2) is right......."
that #1 refers to being right
that #2 refers to the issue or statement previously mentioned by someone