I have checked in early many times at various hiltons and never had a problem (at varying HHonors levels over the years). I have done early morning, but but 4 a.m. sounds a little extreme.
You may want to ask the hotel ahead of time if you are concerned about it. Probably not a big deal if they are not very busy, but if they are anywhere near full they could have a problem with it.
Great question -- like to hear back if you have any problems doing this (and the hotel's reaction).