This is possible. The easiest way to do it would probably be to change the value that gets returned to the incident and also the field on the incident form that it gets returned to. You can apply a template in a client script using 'applyTemplate(template_sys_id)' so the trick is getting the sys_id value of the appropriate template. I think the easiest way to do this would be to create a new field on the KB table that referenced the template that should be applied. Then you could return the sys_id of the KB article when you hit the 'Attach to Incident' button. That would allow you to query the KB article and get the associated template sys_id. Then you could apply the template in a client script. Here are the steps you have to take to do this...

1) Navigate to 'System Properties', 'UI Properties' and add 'sys_template' to the property with this description...
'By default any system table (starting with "sys") can't be reported off of.' You need to do this so that you can create a reference field to the 'sys_template' table.

2) Personalize the 'kb_knowledge' form and create a new reference field called 'Apply template'. This field should reference the 'Template' (sys_template) table. This is the field that you need to populate with the template that should be applied for a specific kb article.

3) Personalize the Incident form and add a new reference field called 'KB article'. If there is a possibility that this functionality should be made available to other task types in the future you probably want to add the field at the task level. This field should reference the 'kb_knowledge' table. Because this modification uses client scripting, this field always needs to be on the Incident form for things to work like they should. You may choose to hide this field with a UI Policy though.

4) Navigate to 'Knowledge base', 'Properties' and change the 'Copy attached content into this field' property. You want to return the attached content to the new field you created on the incident table ('u_kb_article').

5) Now the 'Attach to Incident' button will populate the 'KB article' field on the incident with the KB article you are attaching. Using a client script you can access anything about that article and put it on the incident form. Here's an 'onChange' client script that you can put on the incident table to run when the 'KB article' field changes. It populates the 'Comments' field with the KB article text and applies the attached template.

function onChange(control, oldValue, newValue, isLoading) {
  if(newValue == oldValue)
    return;
 
  var article = g_form.getReference('u_kb_article');
  var kbText = "Knowledge article " + article.number + ":\n" + "[code]" + article.text + "[/code]";
  g_form.setValue('comments', kbText);
  if(article.u_attach_template){
    applyTemplate(article.u_attach_template);
  }
}