Can I play sims 3 by using both discs and digital origin copies?

I have all my expansion packs for the sims 3 on Origin, but when I tried to add my Sims 3 base game to Origin, it says the code has already been used. However, the Sims 3 base game doesn't show up in "my games." I tried to contact EA for this problem, but they have never answered my via live chat and I can't find another way to contact them. I've been sitting all day on live chat, trying over and over again, but no one ever comes to answer my question. The wait time says less than 5 min, but I was on for over an hour and no one contacted me. I give up.

I got a new laptop and I want to move all my sims 3 games over to it, but since I don't have an optical drive installed into the new laptop, I wanted to download my games via Origin. That way, I can play my sims 3 games without need an external optical drive (which I have). But since I can't find my sims 3 base game I won't be able to install it without using the disc (I have disc versions of all my sims 3 games).

So, to get to the point, I'm wondering if I can install the sims 3 base game to my new laptop using the disc, but then download/install all of the expansion packs to the laptop using my digital copies through Origin. Since you need to use the newest game to play, I was wondering if I would be able to play the games from Origin even though the base game would be installed via disc.

Hopefully this all makes sense. It just sucks that EA has some of the worst customer service ever. Even Time Warner is better than them.