Interestingly enough, I was on the phone with tech support on Monday to deal with a separate issue. I asked them this question too, just to see what I would get for an answer. She confirmed that I could not charge the mobile order to the room. However, she was explaining to me what buttons to push to apply it to a Dining plan credit. Which, of course, is not a thing. Not yet anyway. So, perhaps they are close to this happening if the support people already know the process for which you would be doing it.
Either way, I still don’t have the dining plan for this trip, and still plan on charging meals to the room and then paying them down with gift cards. I will probably do at least a few mobile orders just to try it out. However, by purchasing the gift cards with our Target Red Card we saved 5% and will definitely be saving enough over the course of the trip on meals to make it worth standing in most lines.