You are asking the wrong question here.I knew someone who was a nurse in a similar situation she pleaded guilty, received a fine, and it did not appear on her Enhanced DBS
It may or may not appear on an Enhanced DBS - as I understand it the decision about whether it gets included depends on many factors including the role which you are in.
Irrespective of whether it appears on a nurses DBS, they are required by their regulator to self report (and may well have to report to their employer as a condition of employment):
Criminal convictions and cautions
The nurse you mention may have not reported themselves, but they will get into very big problems in the future if this is ever found out (far worse than just declaring a minor byelaw conviction)