Yes, they would be able to see the record, but it would not be counted as a conviction. The link you posted yourself supports what I am saying. This specific type of diversion does not involve any plea of guilt or anything related.
https://www.uscis.gov/policy-manual/volume-12-part-f-chapter-2
"If the accused is directed to attend a pre-trial diversion or intervention program, where no admission or finding of guilt is required, the order may not count as a conviction for immigration purposes.[10]"
I am fully aware of the importance of the partnership and communication in a relationship. That will not be an issue. The focus of this thread is regarding the legal process itself of obtaining the Visa in this situation.