Perhaps not coincidentally, the first time I heard the overture from 6DOIT one of my immediate thoughts (aside from "damn, this is cool!") was: this is really "Disney."
I'm no expert, but I suspect that Disney has all sorts of licensing and copyright restrictions on what they can play, so I'm guessing it's probably more likely that DT were inspired by broadly Disney-esque music when they wrote the overture than the converse, namely that Disney has played DT's music in their parks (though the thought of tearing down the Matterhorn ride with TDEN blasting at full volume in the background sounds pretty freaking rad!).