Yes. HDMI technology has been designed to use standard copper cable construction at long lengths. In order to allow cable manufacturers to improve their products through the use of new technologies, HDMI specifies the required performance of a cable but does not specify a maximum cable length. HDMI Org. have seen cables pass "Standard Cable" HDMI compliance testing at lengths of up to a maximum of 10 meters without the use of a repeater. It is not only the cable that factors into how long a cable can successfully carry an HDMI signal, the receiver chip inside the TV or projector also plays a major factor. Receiver chips that include a feature called "cable equalization" are able to compensate for weaker signals thereby extending the potential length of any cable that is used with that device.
With any long run of an HDMI cable, quality manufactured cables can play a significant role in successfully running HDMI over such longer distances.