Can league be played entirely by keyboard???

maybe, I'm not sure but there could be a way to change the moving scheme to something like wasd(though i'm not sure) it might help some, the only problem would be skillshots.

well ross played alistar with bongos so maybe?

realistically, no. On a few champions, yes. I remember BoxBox playing Riven with a controller and he did fairly well.

I don't think a keyboard has enough range of motion to actually be useful for league.