No, probably not. If you truely have a L1A1 lower then it will NOT work. The easiest way to tell is to note the rear of the reciever/front of the stock. If yours is straight from top to bottom then you have a metric lower and the SAW stock will work. If yours has "ears" that come out on the bottom edge of the reciever then it's an inch reciever and it WILL NOT work.
The handguards are interchangable between inch and metric. The pistol grips and stocks are not. Just as an FYI, the SAW stocks are developing a reputation as a cheek bruiser.
As far as replacing the thumbhole stock, the grip bushing usually needs to be replaced as they were usually mangled or removed. The good news is that it's a cheap and easy fix. Check Gunpartsguy or Gunthings for the bushing. The trigger assembly is unaffected.
HTH,
Mike