Not directly. Geneious Prime and its shared database solutions do not currently provide an API to access data directly (such as REST). However, several less direct options are available for integration. These are covered in What is the best way to integrate with a LIMS?
If you require this functionality, please contact us so we can understand your needs better.
Note: While the Geneious Prime share database is backed by a relational database, we do not provide technical support for direct access via SQL. The schema is undocumented and subject to change at any time, without warning, so we strongly discourage this.