Unless the game has changed significantly, though, there's some really important shit that's governed by the luck stat. AFAIK if the ability to raise luck was removed, there is some especially sought-after equipment that would be a lot less useful.
Dunno if it's okay for me to mention specifics. If you search the forums you can see Gerik's player (Lujan) complaining about it, though. That would need to be changed.
If you leave the raising in, and hide the stat itself, people will be able to tell where they're at by the UE curve, so that kind of defeats the purpose of hiding it in the first place.
Giving newbies a boost to luck during their immunity period would be pretty cool though, as well as randomizing a character's initial luck pool.
Another way I could see something like this working is by having the luck stat vary wildly day by day. Maybe one day you have next to no luck. The next day you're at like the 15UE curve point. All at random. Then, you could hide it, take out raising and add a real big chunk of unpredictability to the luck system.