FWIW, I just raced my first CX race yesterday (Cat 4) on a 15-year-old Trek flat-bar hyrbid bike. Only mod was was a pair of Crank Bros. Candy pedals. I even used the stock, semi-knobby tires -- I'd removed them long ago and replaced them with slick road tires, so I unearthed them out of the garage attic and spooned them back on. I finished 36 out of 42, but I met my goals -- see what CX is all about, have some fun, and finish the race. I guarantee it wasn't my 25-lb. steel hybrid bike that was slowing me down!
There were several hybrid and mountain bikes in the lower classes. There were quite a few regular roadbikes as well, since the course was mostly grass and there was almost no mud.
My advice, from one newbie to another, is to spoon a set of cheap CX tires on your Giant and have a go at it.