No, by agreeing to have a Penalty Notice for Disorder (PND) and paying the fine you will not receive a criminal conviction. Accepting and paying the fine is not an admission of guilt but discharges the possibility of the creation of a criminal record.
The fact that you have been given a PND will be recorded on the Police National Computer but it will not create a criminal record. The information is recorded for administrative purposes and also to establish if a person has had more than one PND.
If a criminal records check is carried out it does not automatically mean that the PND would be disclosed. However it could be referred to if the behaviour that led to the PND was linked with the reason for the check.