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Ok, I just caught an abra just outside cerulean city, just before mount moon, and I want to train abra up and evolve him by kadabra by the time i get to the next gym.
This or you could train him up until he learns a decent move other than teleport(confusion at level 16 I think) so he can fight his own battles. By the time he's learnt confusion he's evolved into Kadabra anyway.
You can't forward game time in Leaf Green, but that's not how the daycare works anyway. Your Pokemon gets an experience point for every step you take while it's in there. So, even if you left your game on for a couple of days, your Pokemon would still be in the same state as it was when you dropped it off.
I think the switch-off routine is probably the best for where you're at in the game. But it is annoying and time consuming :/. When you DO get to the Daycare area, however, you should drop off Abra so it levels up faster. My recommendation is to train Abra through Mt. Moon, Cerulean Cape, and Misty's Gym. It should be around level 16 by the time you are done.