We are a pre revenue early-stage mobile app startup
I've personally been accepted into two accelerators.
The wait time depends on the accelerator. For one accelerator, I didn't hear back until at the absolute last minute (the week before it started). For another accelerator I heard back about a month before it started.
In terms of improving your chances for an accelerator, having an alumni give you a reference is a big help. Also continuing to show signs of traction and growth is a big help as well. There are a handful of other ways to get the attention of the decision makers at the accelerators too.
Call me if you need help getting into an accelerator.