It's possible. I was trying to achieve an identical UI to what you have shown, and was stuck until I tried something pretty simple but a bit confusing as well.
What I've done is set a Spinner as my custom view for the ActionBar, and then:
ActionBar actionBar = getActionBar();
actionBar.setNavigationMode(ActionBar.NAVIGATION_MODE_TABS);
Here's an example of what I mean.
Tabs Code:
ActionBar actionBar = getActionBar();
actionBar.setNavigationMode(ActionBar.NAVIGATION_MODE_TABS);
actionBar.addTab(actionBar.newTab().setText("Today").setTabListener(this));
actionBar.addTab(actionBar.newTab().setText("List").setTabListener(this));
actionBar.addTab(actionBar.newTab().setText("Month").setTabListener(this));
In the parent activity for this activity, I've done this:
Context contextTheme = new ContextThemeWrapper(this, R.style.ActionBarSpinner);
Spinner actionBarSpinner = new Spinner(contextTheme);
// Specify a SpinnerAdapter to populate the dropdown list.
actionBarSpinnerAdapter = new ActionBarSpinnerAdapter(actionBar.getThemedContext(), dropdownValues);
actionBarSpinner.setAdapter(actionBarSpinnerAdapter);
// Set up the dropdown list navigation in the action bar.
actionBarSpinner.setOnItemSelectedListener(this);
actionBar.setCustomView(actionBarSpinner);
This effectively makes gives me a custom view for the ActionBar, but then I can set the navigationMode to tabs to allow me to have the tabs I want. Set the appropriate event listeners on each item, and voila!