Tsubasa means wings (not bird), and Taiyou means sun. No it is not related to Icarus. This episode is almost like a tongue-in-cheek joke about Ichigo and cliffs. You’ll see what I mean if you keep in mind who voices Tsubasa. And the title “Taiyou ni Moero” could be a reference to any number of things including “Taiyou ni Hoero” or “Moero! Taiyou”, old Japanese films and shows. They aren’t important to the plot though.