Hmm. I'm generally skeptical of "thing X reminds me of thing Y so must have been inspired by it" arguments, since similarities happen all the time through chance or through drawing on a common pool of cultural influences. But this is actually a fairly plausible and well-reasoned hypothesis. If it's known that Roddenberry did listen to those radio shows -- and it seems likely that he did -- then it stands to reason he was influenced by their ideas, consciously or otherwise.
On the other hand, as I mentioned, the first time Spock refers to himself as a logical being is in "Where No Man Has Gone Before," which was written by Samuel A. Peeples. So it's possible that the inspiration for making Spock and his people logical came from Peeples, not Roddenberry. A common mistake these days is to assume Roddenberry was a singular auteur. TOS was made in an era when TV writing was highly freelancer-driven, and the show's producers and story editors contributed a lot too. For instance, Paul Schneider created the Romulans, Gene Coon created the Klingons and possibly the Federation and Prime Directive, D.C. Fontana and Theodore Sturgeon created most of what we know about Vulcans, etc. So it might be worth examining Peeples's background and influences.
So what you're saying is it's a logical fallacy?
