No, I wouldn't use any drywall compound, just fill it with thinset and the special tape for thinset (cbu) installs. You can do this while tiling, or, if you prefer, you can do it before then let the thinset cure. You might be okay if you used a setting drywall mud, but it's a little risky if you use the stuff premixed in a bucket as the added moisture when you do use thinset to tile could soften it. It somewhat depends on the size of the tile you are using...if the tile are big, they'd bridge the gap caused by the tapers at the edges of the board. If they are smaller, it is harder to get them to lay flat. in no case do you want to have a hump over that joint like you typically do when painting over it; the tile won't lay flat.