I have my app installed on two development devices, one iOS and one Android.
If I send a push notification from the ACS console with badge set as "+1" then all badges increment as expected.
If I send exactly the same request via the REST API the badge is unaffected / not incremented.
{badge":"+1","alert":"Test"}
If there is a badge number e.g. '2' this remains as '2' The count number in the Android notification also remains unaltered unless the Push message is sent from the console.