Snowboarding as ski training?

Would it be beneficial to your skiing to learn how to snowboard, or would the movement differences cause conflicts?

I don't think it could hurt.  It's interesting to learn how the board turns. I've only done it a few times, but it is pretty easy.

Therusty snowboards a lot, maybe he'll have a better answer for you.

My ears were burning ....

Regular snowboarding won't teach you movements that transfer over to skiing. There are some similar movements (lateral tipping, fore/aft [heel/toe] pressure management, rotary movements, etc.). But because everything is basically rotated 90 degress, the results/feedback does not transfer to skiing very well. What does transfer is the feel of carving. Once skiers feel a snowboard carve, the "oh, now I get it" light bulb goes on. After that, snowboarding becomes just sliding differently on snow.

Alpine riding (typically with hard boots, plate bindings and aggressive forward stance angles) is done a little different than regular snowboarding. The movements are closer to skiing, but still done differently.

For most people, snowboarding movements won't mess up your skiing, say like tennis and racquetball conflict for most people. But many skiers do have to fight through skiing muscle memory when learning to ride (because movements that make you go forward in skiing make you fight the edge while riding). I struggled horribly when I started riding. It was not until I got my own gear, rode in soft snow out West and then got decent coaching that I got over the hump. Now, most of my days on snow include a seamless switch from one set of gear to the other.

Your background in other sports can also have an effect on this. The more experience you have in sideways sliding sports (surfing, skateboarding, etc.) versus forward sliding sports (skating, blading, etc.) the more you're likely to favor riding versus skiing. The less relative experience you have in other "opposite movement" sports, the more likely you're first experience will be difficult. To some extent your question is like "Will roller blading mess up my surfing?". For most people, the answer is "not really".