Yes, you will get bleaching. If you work under the same darkroom light conditions long enough, you can eventually judge a snatch point that will bleach back to where you would like it to be. That said, I have found that even massive amounts of exposure won't flatten the print out enough. Please try pre-exposing the paper, and I don't just mean flashing it. I use a portable light box for anywhere from 5-15 seconds, in addition to massive exposure. All papers are different, but I think the value of pre-exposing (or post exposing . . .sometimes I do it in the developer tray at early stages of development) in lith is underappreciated.
If you take a look at my gallery, most of those prints have been pre-exposed to some degree.