Can race exhaustion lead to illness?

Yes. After previous Marathons and a half ironman distance tri, I have gotten sick with whatever was floating around at the time. If your body is stressed and you have worked out really hard and been on the "edge" in terms of exhaustion, it is usually the time you will get sick. I have never been sick after a race as short as an Oly, but don't see why it wouldn't happen if all of the conditions are "right" for getting sick. I just ran a marathon though a week and a half ago and this is the first time I didn't get sick. I did though do all of the right things (nutrition wise and rest wise) though this time both before and after that I hadn't done before.

My guess is that you were already coming down with something, but not having symptoms yet (and it's easy to attribute minor things like poor sleep or sluggishness to taper, anyway), and then actually noticed it the day after the race. Plus it's possible, if travel to the race or time in crowded public places (packet pickup?) was involved, that you got exposed to a cold/flu bug at that time, and it takes a couple of days for symptoms to appear after that. .That a race happened to come in between may have been coincidental, or it may have been one of several stressors (along with change of routine during taper, limited sleep before the race, etc.) that might have lowered your immunity enough to get sick. There is some evidence that long races, like IM or marathons, can lead temporarily lower immunity, but I don't know if any Oly falls in that range or not. Timewise, maybe, in terms of stress on the body, not sure.

One other possibility, if symptoms are only sore throat, body aches, and/or GI issues, dirty water? I've had similar symptoms after some of my races here in Vietnam--the giveaway is when other people who did the same race, or friends/family who just went swimming, have the same issues.

Went to doctor today and I have strep throat. I was so sick she gave me an antibiotic injection rather than oral meds.

Ouch, well you probably were exposed prior to the race and I don't think an OLY would put you over the edge, but hope you are feeling better now.