Yes. Flights which have already posted when you sign up will not count, but even flights taken already but not yet posted to your account will count towards your challenge.

I actually squeezed in my Gold Challenge request about 18 hours after 2.5 days of flying (to grab the elusive -- now apparently impossible -- Double Challenge) at about 5:30 in the morning (had just arrived at my resort for a week vacation after first, and looong, Mileage Run -- six RTs plus positioning flights w/ complex re-routing to fix very tight schedule after mechanical on first flight; but after that it was smooth as they were RTs on the same equipment doing turnarounds, so I knew I could not miss my next flights ). I finally nabbed a CS who didn't double check my account to see that I was already signed up for the Platinum Challenge, so I was able to start earning the 25% RDM bonus and miles towards upgrades in the middle of that (already completed) MR when they posted within a day after the call.

Steve