If you did enter this on SCH E, the depreciation and other expenses would get your taxable rental income to zero anyway, with no excess losses allowed or carried over. So you would not pay taxes on that rental income, weather you entered it or not.
However, if you live in a state that taxes personal income and offers a "renter's credit", and the tenant wants that credit, you may have no choice but to do the SCH E, even though the reported rental income would not be taxed in the end.
If your property is in the state of Hawaii, then you have to report it, as HI assesses a GET tax (GET=General Excise Tax) on the gross rental income before "any" deductions are taken.
