I guess you could, although I'm not sure why you would. I just joined EC myself, but my understanding is that it allows you to bypass standing in line at the counter. Can't see why you would give that up, (or even spend the time at the counter having them add your number) but to each his own.
If you made the reservation through some other site, like Expedia or Orbitz, you may not be able to earn points for the rental, but you can call National directly and have them add your EC number to your ressie so you can still bypass the counter.