Is it possible to find out if an Android application runs as part of an instrumentation test

A much simpler solution is check for a class that would only be present in a test classpath, works with JUnit 4 (unlike the solution using ActivityUnitTestCase) and doesn't require to send custom intents to your Activities / Services (which might not even be possible in some cases)

private boolean isTesting() {
    try {
        Class.forName("com.company.SomeTestClass");
        return true;
    } catch (ClassNotFoundException e) {
        return false;
    }
}

Since API Level 11, the ActivityManager.isRunningInTestHarness() method is available. This might do what you want.

If you are using Robolectric, you can do something like this:

public boolean isUnitTest() {
        String device = Build.DEVICE;
        String product = Build.PRODUCT;
        if (device == null) {
            device = "";
        }

        if (product == null) {
            product = "";
        }
        return device.equals("robolectric") && product.equals("robolectric");
    }