ANSWER: Yes, assuming the "Bypass Security" flag is checked in the Scenario Details. Although duplicates will be detected with "Bypass Security" checked, if the user does not have access to a duplicate record, they will receive an insufficient access rights error when they try and view the records. They will also not be able to merge the duplicates from a Warning.
More information on Bypass Security can be found HERE.
If the scenario is set to Auto-Merge or Auto-Convert, the records will be merged or converted. If an Opportunity is created as part of the conversion and the Opportunity Owner is set to either Lead Owner or current user, they will have read only access to both the Contact and Account, due to the Opportunity being owned by them.