Theoretically, it should be possible, so I am sure it's also possible in practice. Now, it may make the bar softer, but hopefully this obstacle can be overcome by tweaking the recipe.
Yes, if you add too much citric acid, you will achieve a "mess", which it isn't caustic. Just greasy.
My guess would be that whoever has tried and failed has used too much citric acid. We are trying here only to tweak the pH down a little.
It's not easy to find out how much citric acid to use. If you go by trial and error, you should
Something else: I believe the citric acid must be added in a water solution and only after the soap is done. Which means HP or rebatch.