Hi,

Yes it is possible by creating a client action for the menuitem.

For live examples you can refer the apps below

https://apps.odoo.com/apps/modules/13.0/hrms_dashboard/

https://apps.odoo.com/apps/modules/13.0/base_accounting_kit/

For example you can refer the code below.

Create a js file

odoo.define('model_name.action_name', function (require){
"use strict";
var core = require('web.core');
var AbstractAction = require('web.AbstractAction');
var NewAction = AbstractAction.extend({
    init: function(){ 
    this.function_name(); 
    },
    function_name: function(){ 
    //Write the code here to preform menu item click.
    });
core.action_registry.add('client_action_tag', NewAction);
});
});

Create a record with model ir.actions.client and specify the record id on menu item action.

<record id="action_menu" model="ir.actions.client">
    <field name="name">Render Template</field>
    <field name="tag">client_action_tag</field>
</record>

<menuitem id="menu_client_action"
          name="Client action Menu"
          action="action_menu"
          parent="model_name.parent_menu"/>