joe: At the elevations you're talking about you're probably not at risk of medically dangerous altitude sickness (HAPE or HACE) unless you are pretty unusually susceptible to altitude sickness. It's very possible, particularly with exercise or if you're sleeping at the upper end of those elevations, that you'll experience Acute Mountain Sickness. Wikipedia has extensive information, but at the mild end of the scale you mostly feel weak, have a headache and a reduced appetite.

Acclimatization is of course ideal, but I'd bet you can reasonably try as long as you listen to your body. I like a little extra caffeine if I'm experiencing mild altitude sickness (for me this is around 11,000ft, living at sea level, and spending my summers at 6,000-7,000ft). A difficult thing can be forcing yourself to eat enough. As road cycling is heavily cardio dependent expect for the climb to be much harder, but isn't road cycling a little masochistic anyways?

So yeah, probably try it out and listen to your body. Obviously training is a good idea also.