I emailed the organizer to get more information about how this works with the pushups. Here is what I found out
"We will start with the run (3 miles), then straight to Swim (300 yards) and when you are done we will stop your time. When you will get to the push ups-station we will take 2 seconds off your time/each push up done properly! Push ups are judged by our personal trainers and they are performed according to American Council of Exercise (ACE) standards (where you go to ‘about’ 10 cm off the ground; chest almost touching). Women can choose to perform modified pushups."
After running and swimming, I'll be lucky to do 2 proper pushups, but maybe more modified ones. But based on the way this works I really don't think the push-ups will be much of a factor and shouldn't stop someone (me) from doing the event. Here's why I say that. Let's consider three scenarios: 100 pushups, 25 pushups, and 0 pushups. The 100 pushups will be worth approximately 3mins 20 seconds off your time, 25 pushups will take 50seconds off your time, and 0 pushups will mean your time stands.
I'm going to have to check my calendar, but this is almost too unique to pass up. I'm definately considering signing up! Normally I do "real" pushups, but I just might practice modified ones just for this event.