Since no one really seemed to answer your question, yes invites are done through the Origin overlay. I've had no issues with it, the overlay works and I was able to invite and be invited last night. Make sure the overlay is enabled in both the Origin general settings and the specific game settings.
The store itself was great and I was able to purchase all of the items I intended to but jesus fucking christ, the clientele. I went a week without food, motherfucker, and you're complaining about the color scheme of that backpack?!