Honestly, I'm not sure "Roddenberry-esque" is the best word for diverse casting, since if you look at his overall body of work, he wasn't as inclusive as he liked to claim. "The Cage" had no ethnic diversity at all in its main cast, and part of the reason NBC asked for a second pilot with a new cast was because Roddenberry had failed to deliver the diversity he'd promised them. His Genesis II does have one major black lead and an Indian character named Singh (which seems to be the only South Asian name Roddenberry knew), but it also had Ted Cassidy as a "white Comanche" wearing brownface makeup and speaking broken English. The second pilot for that concept, Planet Earth, lost Singh and reduced the black character to a minor role, and though Cassidy's character lost the brownface and spoke coherent English now, he was still called a "savage" by one of his colleagues. In The Questor Tapes, there are no nonwhite cast members aside from James Shigeta in a minor role, and one character, on being told that the title android has adopted a medium-light skin tone, says "So he looks normal." And as far as I can tell, Roddenberry's 1977 Spectre pilot had an all-white cast, as did the first feature film he wrote and produced, Pretty Maids All in a Row.
To Roddenberry's credit, he did try to tackle racial prejudice in an episode of his first series The Lieutenant (where he first worked with Nichelle Nichols), and his frustration at the network's refusal to air the controversial episode did help inspire his decision to do a science-fiction allegory with social commentary. And his unsold pre-Trek pilot Police Story did have a black second lead, Rafer Johnson. But considering his whole body of work, it doesn't appear that ethnically diverse casting was really something that can be called a Roddenberry trademark, not consistently anyway.
