You know the Champions league game is always a game that can not be predicted because of the the kind of teams that are always present in the league with good experience. It is possible for Bayer Leverkusen to make the competition to be interesting but it is hard to predict if they will reach the finals. The competition in champions league is always tough, strong teams don't joke with champions league most times it is common to see teams like Real Madrid, Manchester City, PSG, Bayern Munich at the end of the competition, these are experience teams that are used to champions league. Bayer Leverkusen have a good coach but I'm not believing it will be the reason for them to get to the final.
Just as you mentioned, Champions League is different from any other tournament in the club side, it is the biggest competition in the Europe and the best teams in the world do compete in the Champions League; I don’t think Leverkusen can be mentioned among the favorites to win the title despite their performance in the just concluded season.
Leverkusen is a good team with team work I must say, but rating them above teams like Manchester City, Barcelona, Inter Milan, and other big teams in the Champions League is not proper because these teams can do better than Leverkusen in the Champions League.
On the other hand, Leverkusen can still display and outstanding performance in the Champions Next season just as they did in the Europa League, but it will be very difficult for them to reach the final.
In football, it's easier to defy all odds and have a great season but maintaining the impressive performances and results of the same same season is actually more difficult than than winning all the trophies. Bayer Leverkusen last season were simply one of the best clubs in Europe as they even went on to win the German Bundesliga as well as the DFB-Pokal. Bayer Leverkusen's only defeat of last season was the one they suffered in the hands of Atalanta in the UEFA Europa League final.
Next season, they'll have to defend their title as well as live up to the expectations of their club fans of which I think will be more demanding than that of last season. Bayer Leverkusen in my own opinion will do well in the UEFA Champions League competition but I don't think they'll be able to go past the quarter final stage of the competition.