Like others mentioned above, its pretty boring, and a road race just zooms by you. I do attend track races at the Carson Velodrome here in Southern California - a top-notch indoor facility built after the 1984 L.A. Olympics with about 6,000 seats and air conditioning. Much more interesting watching the indoor pursuit and time trial races since each races goes by pretty quickly. Even if it was an outdoor track I'd probably go watch races there, just more to see and get excited about vs a road race.
FWIW: The Tour of California (in May) does get pretty good crowds around the finish area and on some of the loops and climbs.