I think that it would be a lot harder for an orphan to trace their genealogy, but not impossible.
In the sense that there are no family members left to ask family information of, then that is hard, as even the slightest bit of help is still help.
On the other hand, even an orphan will have a birth certificate, as in most countries if not all, will have a system where everybody's birth will be registered in one way or another, and this is where I feel would be the first place to start for an orphan to trace their ancestral roots.
It will probably take longer to do the search, as one person searching would obviously take longer than a whole family helping to search, but it's certainly not impossible.