NO.

I mean your employer probably has a set of books, but that's not true in your own local set of books.

In your local set of books you would have something like:

    ACME, inc Employment Income  $100 DEBIT
    Bank Account                 $100 CREDIT

When you send a payment to your Power Company:

    Power Company Expense: $100 CREDIT
    Bank Account:          $100 DEBIT

I agree with your first two paragraphs but not with this last one. When money leaves you or comes in from an external source, there is always some proxy account for that external party in your own books. And the whole situation is mirrored in the accounting system of the external party (unless they are a consumer). Each party records two entries.

Yet accounting is necessary because money is created out of thin air. Money is just the representation of debt, an IOU. There needs to be a record of it in order to know that a debt was created and that a debt was destroyed.

More practically, let's say you give me corn today, and I promise to deliver some of the chickens fed that corn to you after it is ready to for slaughter. Money keeps track of the promise outstanding. We record that promise, or account for it if you will, so that we remember that there is a promise and so that we can later ensure that the promise was delivered upon as agreed. Something that becomes especially important when you realize that promises can be traded on to other people who weren't party to the initial deal. Perhaps you don't really want chicken, but would prefer a watch instead. Luckily the watch maker would like to eat chicken for dinner down the line, so you give him the promise of chicken in exchange for the watch. So on, and so on.

Realistically, double-entry accounting is really quadruple-entry accounting. You record that something was received and you record that a promise was made, then, later on, you record that something was delivered as promised and also record that the promise is no longer outstanding (or in reverse if you are on the opposite end of the transaction). A profit indicates that people still owe you things that you haven't collected upon. A loss indicates that you still owe people things that you haven't yet delivered.