I have a check to cash, of quite high value (<$500,000). Would it be possible to go to a bank counter and get the check instantly cashed to my account?

You cannot cash the cheque immediately, instead, they will issue you a confirmation slip that your deposit is confirmed.it will most probably only appear in your bank account for use the following day after 12pm.

Of course, you can bank in the cheque at the counter. It may take a little longer to clear the cheque though.