Will we be seeing more of the Savoys later on? Or is their screentime based on their time spent with Mordecai, like in the pilot?
You'll be seeing more of them. There's a fairly extended flashback to where they came from in Season 1 (before they met Mordecai).
We have other animated shorts planned for them as well.
This arena got everything: birth records, baptismal records, records of death, my own birth, absolute birth, a shining place in the absolute darkness, a gold plated Shangri-la, day and night, paradise lost, Sodom, endless darkness. The Apocalypse.