No, its not impossible. What will happen is if you get the "we are experiencing a high number of calls" it will just hang up on you. It will not put you on hold. You can call 10-15 times in a row and this can happen over and over, which is frustrating. When you do get through there is typically an additional 15-30 min wait before talking to someone. The person you will talk to is a call center agent NOT an immigration officer. The agents have limited information and are often reading from a basic guide that can be found online. They do not always have the most up to date or accurate information so you have to keep these things in mind.
They are able to tell you SOME things...like if there is a note on the file asking for additional info, or if your Sched A has been attach (they were able to tell me when I called) but the won't have access to a lot of other information about your application.
I might call them tomorrow to ask if they accepted the sche. a and pcc we uploaded since we never received confirmation email they accepted them only got email about file transferred to vo .