You can surely shoot without the peep,but as has been mentioned,it will take a concerned effort to make sure that you anchor EXACTLY the same EVERY TIME!For me this is not as easy as it sounds,especially under hunting conditions.The peep site is merely another reference point,this is true enough,but imagine if you will,shooting your rifle with ONLY the front site as a reference point.How do you think your accuracy would turn out?I know that most bowhunting shots are at close range,but we owe the animals we hunt the respect to be the best shot we can be,don't you agree?
I personally hate a peep-site.I ream mine out to gather more sight picture and take in as much light as possible.They always seem to twist,get water in them or something else that ticks me off.I'm looking at some of the alternatives around to find something that I'm more happy with.Time will tell.Good Luck!
Later.....whackman