In general, you would be billing expenses to your clients so that you can be reimbursed by them. For example travel expense (mileage) or if you had to purchase something for them like a Hard Drive that they would need to pay you back for.
However if you wanted to keep track of any expenses for your own use, then yes, add yourself as a Client and put the expense there. Then you can run a Report at the end of the year on yourself.
