Yes. 

When you enable Can be Merged, an Odoo Server Action is created for that model.

You can adjust permissions via the Allowed Groups field. 

In Developer Mode, find the relevant Merge Action via the Server Actions Menu at Settings --> Technical --> Actions --> Server Actions.

Here we have set Can be Merged to True for Helpdesk Tickets:

By default, Allowed Groups is set to those in the Administration / Settings group, but you can delete this group and add your own group or groups to manage which Users can use Merge.