Yup, you can easily switch between them. There are 2 support slots actually (1 for Combat and 1 for dungeon crawling).
Actually, it's the other way around. Random battles won't require Rise's Spotlight ability since most enemies are slower than the PCs, and free healing from Fuuka is rather nice. On the other hand, the ability to move before bosses is invaluable. You can do all sorts of things like set up buff spells immediately (useful against heavier bosses), Power Charge on a slow fighter and guarantee they land a hit next turn, and even emergency heal if your healer is slower than the boss. They're also pretty useful against FOEs, since if you're not strong enough to fight one you can have all 5 of your PCs attempt to run away before getting rolled.