Leaving the moral issues aside, what you're thinking of doing is illegal: For 'homeland security' reasons, all hotels in Italy have an obligation to communicate the names and passport / ID card details of all guests staying in their establishment to the Carabinieri – so by not declaring an additional person you would certainly be committing a criminal offense. Also, all hotels in Rome now collect a daily tourist tax payable by all guests, which is passed-on to the city administration – so by sneaking-in a non-paying guest you'll be committing your second criminal offence. As you would also be stealing from the hotel, if you get found out, you should be in no doubt that the Carabinieri would be called – so if you go-ahead with your plan, don't be at all surprised if you get a rap on the door from a couple of uniformed officers carrying pistols.
bdemaria is absolutely correct, and the cost of an additional person would not normally cost the earth. You may have to pay a small supplement for the upgrade to a room with the extra bed / sofa bed; and for the extra breakfast and tourist tax.
… and 'not leaving the moral issues aside' – (and I hope I'm not contravening FT etiquette guidelines here) – if you try it on and get found out, you probably deserve to pay the consequences.