Question: Is it possible to send silent push to os x client from API request or with the web?
Answer: There are no "true" silent pushes in Mac OS. If an app is closed, pushes will not be handled. However you can imitate silent pushes by not setting any alert in your request and by adding required parameters to mac_root_params:
Actually you can specify any other parameter instead of content-available, the only necessary step is not to set up an alert. And, on application side, it will still call the following method:
- (void)onPushReceived:(PushNotificationManager *)pushManager withNotification:(NSDictionary *)pushNotification onStart:(BOOL)onStart
This solution only works in an opened app.