I did a closer-only in a public Yahoo league a few years ago. Came in first, but here is what I did...
First, you need two STUD starters. I had Randy Johnson and Greg Maddux. I also picked up Rick Ankeil and Kerry Wood (his one & only good year...). That trio (Johnson, Ankeil & Wood) gave me a shot at strikeouts, and kept me in the middle of the pack in that category. They were all excellent with ERA and WHIP.
Second, I had 3 of the top 5 closers, and 1 other top 10. If I remember right, it was Hoffman, Nen and Urbina, with I think Zimmerman (yeah... it was a while ago). The good thing about those guys is tha they all pitched regularly and had a decent number of strikeouts.
Third, I had a couple of great WHIP guys - like Dotel & Arthur Rhodes. People that wern't closers but gave great numbers elsewhere.
The idea was to SAVE money on starters (well, I'd use two of my top 5 picks on starters, but then nothing else until past round 12) and get a monopoly on the great closers. That will guarantee you win Saves, and give you a solid shot at ERA and WHIP. With a heavy strikeout guy you won't be in the bottom 1/3 of the league in Ks either. That give you (in roto terms) a top flight pitching staff, giving you top marks in 3 of the 5 categories and top 1/2 in one other category.
Your team just doesn't have that... You have ONE top flight closer, and 2 ranked somewhere in the 8-15 range, then another 2 in the bottom half of the league... just not enough to dominate all three categories (S, WHIP, ERA). If they all hold onto their jobs, you'll probably win saves just by sheer numbers though, but a team with (perhaps) Rivera and Nen might beat your entire staff and post better WHIP and ERA.
To top that off, your hitting is weak for a 12 team league with only one star pitcher. My prediction would be bottom third of the league for this team... sorry.