Unless my googling skills (which, I believe, are usually quite good) have let me down here, I regret that the answer to your question appears to be "No".
I started off my simply googling 'burpless radish'. Then I added double quotes to force Google to look for the specific string (rather than for the two words separately). I still kept getting references to 'burpless cucumbers' though, so I added in filters to exclude the words 'cucumber' and 'cucumbers'. Despite then continuing to add in further filters, and to use every Google trick I know of, I still couldn't find a single web reference to a 'burpless radish'. So, if anyone has ever managed to create one, they seem to be keeping damned quiet about it!
Sorry :(