I am searching for house I believe to be for sale by owner. I have the address, but I am not sure where to search for a listing or if it even will be listed? Does the owner have the choice not to list?

Sure, but what's the purpose, no one will find it. Google the address.

An owner has free choice on how to promote their property for sale. Generally listing using MLS are done through brokers, not by SBOs.

That is just the point, a sale by owner is almost never put on a MLS listing, since that is done by real estate people.

There is a company called "for sale by owner" I think it is still there, that for a fee lists your home for you,

But normally they put a sign out front, maybe list it on a couple web sites and say they are selling their home

If you have the address then Google it, buy a map or go to the public library and search city records.