There is day and night in Ruby/Sapphire...or rather, time definitely passes. The fact that you have to set a clock at the beginning proves that, and the passage of time can be seen to affect the game in thwe Shoal Cave, where tide goes in or out every six hours.
I haven't checked for myself, but I'm told Eevee will become Umbreon if you evolve it after midnight...I'd love to know at exactly which times it evolves into Espeon or Umbreon, though. Someone care to enlighten us?