I'm assuming in the rose garden or something, right? I don't know if you can just have a ceremony and no reception. I know you can have a reception and not a ceremony.
If you are thinking of an in-park event, then no.
I haven't heard of anyone doing this. If you get married during the week, the minimums are much lower than on the weekend, and it wouldn't be ridiculously expensive to have a wedding and reception.
Have you contacted FTW?