On a serious note, the soap would be probably kill any bacteria, including your mouths microbiome of good bacteria. So, the soap is clean but your mouth risks getting dirtier.
If we abstract this a little, let us say you are washing dishes. You scrub a dish with a soapy sponge, after getting rid of any visible food/stains/etc. Is that sponge still clean after scrubbing? My answer is no, but what is yours.
Also, to clarify, the dish looks clean before you scrub it.