I'm willing to grant that the hypothetical Vulcan would be a little more likely familiar to science fiction readers than to the general public, but still, not that likely. General relativity had gotten quite well-proved a generation earlier and obliterated any need for the hypothetical planet.
But that's the difference between science and science fiction. SF doesn't have to match up perfectly with reality. It's allowed to fictionalize. As I've already said (though I forgot to provide the link -- here it is), Wikipedia lists several stories ranging from the '30s to the '60s -- as late as 1965 -- that used Vulcan as a setting, even though it was disproven in 1915. In the same way that a lot of SF and space fantasy stories went on writing about Martian canals long after they were debunked. Science obliterated the real-world need for Vulcan and the canals and so forth, but that didn't obliterate the literary need for them as story settings.
After all, sometimes science gets things wrong. Sometimes things are debunked by one set of scientific findings and then revealed to be plausible again by later findings -- such as, say, the presence of liquid water on Mars. So if someone wanted to write a story positing that the debunked planet Vulcan actually did exist after all, that wouldn't be entirely impossible to suspend disbelief about, if the story sold the idea well enough.
The question does make me realize, though, that I can't think of any science fiction stories set on the hypothetical intra-Mercurial Vulcan.
See the link above. Wikipedia lists two 1930s stories from Astounding, the Captain Future pulp novels from the '40s, and a '65 novel called Mission to Mercury. It also suggests that it's ambiguous whether the planet Vulcan from Doctor Who's "The Power of the Daleks" (which aired in late 1966, just two months after "The Man Trap" first established Vulcan as Spock's homeworld) was meant to be a solar or extrasolar planet, since it was said to be humanity's first colony, suggesting a nearby world.