Xabi Alonso is prominent enough to handle the hurdles which will be coming his way next season. Remember he's the main reason behind the sudden peak form of Bayer Leverkusen, they're able to comprehend the situations at hand and hitting top target in each season. Bayer Leverkusen have relaxed their players and they're warming up for the big season ahead. This is not an easy one because the entailed actions involves other oppositions.
I also have no doubts about the ability of Xabi Alonso especially for this season again because from what he has shown last season at Bayer Leverkusen to be able to win the Bundesliga is something extraordinary so that it has been a good achievement for him and hopefully can be achieved again this season. However, I do not think that Bayer Leverkusen can easily face the obstacles in the UCL, because it is a competition with quite high tension and very different from any competition including the Bundesliga.
Since being coached by Xabi Alonso, Leverkusen has transformed into a club that needs to be reckoned with by every opponent, especially in the Bundesliga, and Leverkusen's potential to defend the Bundesliga title this season is still wide open, especially since the squad has not changed much from last season's squad. Plus Bayern Munich and Dortmund will start to adapt a lot because both teams are coached by new coaches. But it is true as you said, the Champions League competition will be very different, this is a competitive league and even the atmosphere will feel different so it will not be easy for Leverkusen.
Last season all eyes of football fans were on Leverkusen, because they performed very impressively unbeaten in the Bundesliga only losing once in the Europa League final against Atalanta. This season Leverkusen will try to repeat it again although it is difficult but I believe Leverkusen can defend the Bundesliga title and can go further in the Champions League.