Xenon, from previous comments, it appears that we may be on the same team, or at least running the same courses in Seattle. If you are only doing the fall xc races as training, you might be fine in regular racing flats.
I've had a pair of spikeless racers (a Mizuno pair) and my favorite pair of spikes (Asics Dirt Diva) had both spikes and rubber cleats so I could pick. I didn't get any traction with the Mizuno one, but get moderate traction with the Asics. Sadly, both are discontinued. But Nike makes both spikes and spikeless pairs and I think a few other makers do.
On Upper Lower Woodland, and Lincoln Park (Sundodger), opinion is definitely divided on whether you even need spikes. Woodland is really rocky for half the course and yes, one of the fast masters guys rolled his foot and was pretty badly injured. Jerry recommended that we not wear spikes for Woodland (but I continued to do so). If you are only going to do Sundodger and Woodland, and you aren't planning on nationals, you'd probably be fine in flats.
I've been lucky and I've worn spikes all season and prefer them - and I think I've only done one race per season (usually an early one) in the spikeless kind. On grass courses (or mostly grass ones) I think spikes are advantageous (and safer on slippery courses). I didn't run WWU, but you can ask the other women (and guys) on your (our?) team or Tom C. for guidance. Many wear Brooks, too, so maybe you can borrow a pair to try on?
FWIW, though, spikes are pretty cheap and they often have last year's models on sale. I have way more xc spikes than i have any other racers, but they don't seem to wear out too much.