Yes. However, the process does require using the Salesforce ID's of those records that you're assigning.
When you assign a mobile record to a user, that record and the relevant child records are synced to that mobile user's device, to be used in Jobs. In order to upload mobile record assignments, you need to create a .csv file with each row containing the values below.
|Field in SObjectContactAssociation Object||Value in CSV|
|Contact||Contact Name of the Mobile User|
|NumberOfRecords||Number of records of specified object assigned to mobile user|
|SObjectApiName||API Name of the object the record is in|
|AssociatedIds||A comma separated string of the 18-digit Salesforce IDs of the records to be assigned to the mobile user|
|Instance||Should always be set to '1'|
|UniqueKey||This will be overwritten so you can just populate with 'x'|
- Create a .csv containing a column for each of the values above.
- Use Data Import Wizard, or your favorite Salesforce Input Tool to create new SObjectContact Association records using this .csv.
- Confirm your upload was successful by spot checking Mobile Record Assignment in the Mobile User tab.