Will Trip in the show beat Alder? Probably not, considering they gave him a battle and it was one on one at that. They could always do a full battle like Paul did with Cynthia but what would be the point. If Trip can barely advance in the Unova League Tournament then what makes you think he would beat the Champion, especially when he was just toying with him in his Junior Cup exhibition match.
I doubt it, Trip is a good trainer, but he depends too much on one or two pokemon. He is friends with his pokemon, but he is a bit arrogant like Gary was. And he didn't even make it in the top 100 in the Poke League.
Probably not. The anime is different from the games so that the Champions aren't just people with really high leveled Pokemon, they're actually extremely strong, since the anime allows room for more growth in Pokemon obviously. So no, I don't think Trip will ever beat Alder in the anime just because Champions especially in the anime are way stronger than regular trainers.