Yes, he wrote Facebook himself but only after consulting with Eduardo; not to mention, Eduardo funded the initial servers and such.
So I guess the most realistic hypothetical question would be whether or not Mark and Eduardo would have both been invited for an interview. I'd still say yes. Given their main competition was myspace, their concept of exclusivity was an innovative and clear edge. In essence, at the time, I imagine their goal was to essentially make Myspace irrelevant by making Facebook a friends-only environment.
To address whether or not Mark would have been invited for interview if he had applied by himself: I also think yes to this, purely because YC seems to care about the people more than anything. Mark's track record before Facebook is extremely impressive so I would say AS LONG AS Mark expressed a desire to add members to the team (in the written application) before coming to YC, he would have been accepted.