Its possible but only in case if user will open application from received push. Otherwise application will not get data from Push notification payload.
Update:
The answer posted by @Vineesh is correct. To grab the messages out of the push notification that you receive, you need to implement the didReceiveRemoteNotification method as below
-(void)application:(UIApplication *)application didReceiveRemoteNotification:(NSDictionary *)userInfo
{
NSLog(@"userInfo %@",userInfo);
// you can get the required message as below
NSString *msg = [[[userInfo valueForKey:@"aps"] valueForKey:@"alert"] valueForKey:@"body"];
}