Your suggested story goes into the right direction - since Personal Impact is all about convincing another person about something.
Based on the 1-sentence-summary of your example I cannot seriously tell if it will be a good story at the end of the day - it depents mainly on what you make out of this situation.
Main topics you need to consider when developing your storyline:
1) Underlying conflicting interest
The most basic ingredient for a strong "Personal Impact" example is a clear underlying conflicting interest between you and the other person. Both parties need to have a strong interest in the outcome of the situation with different opinions at the outset. Without this, it will never become a strong Personal Impact example, since if there is nothing at stake, it's not difficult to convince someone, and thus you miss the whole point of this PEI dimension.
2) Showing a strategic, process-oriented view of convinving somebody
Furthermore, it's good if your Personal Impact example is going on at least over several days, even better for weeks, since your interviewer is interested in understanding your approach to convince someone from a more strategic, and not only operational/tactical perspective, having candidates clearly laying out a strategic masterplan on how the other person could be convinced. And that's something which usually doesn't happen in one meeting or over night, but requires time to "design" and execute this process of convincing someone.
At the same time, the specific outcome is not that much of interest - it's mainly about your contribution and impact on this situation!
Hope that helps as a start!