I play in a H2H league where we roster 5 RPs and count both saves and holds. For the past 4 years, I have not once drafted a closer and always aimed for middle relievers with good ratios. I always seem to end the year around 5th-6th in the number of saves since I injuries always seem to create opportunities for guys I've already drafted. Rafael Soriano, Ernesto Frieri, Tyler Clippard all ended with 20+ saves (some even 30+). None of them had closer roles during drafts.
I think you need to differentiate exactly what you are asking though:
No RPs on the roster?
or, no closers on the roster?
RPs are fundamentally crucial to your team. Again, I would need to know the settings of your team (# of managers, categories, roster type). But RP tend to offer elite ERA and WHIP, not just saves. The number of SP who can offer sub-3.00 ERA and sub-1.05 WHIP can be counted on one hand. The number of RP who can offer that same line: 22
My strategy has been to supplement sitting SP with RP's owning elite ratios and high strikeouts. Here's my reasoning:
I'm going to combine 3 RP whom could be had off of waivers / free agency in most 10-team non-holds leagues:
David Hernandez - Ari
Ernesto Frieri - LAA
Darren O'Day - Bal
If I combine their 2012 stats I get the following:
in 201 IP
That stat line would easily beat the #1 SP off any draft board. And I'm not even going after the saves, mostly the ratios. Why? Because it balances the SP who may offer a 3.75ERA and 1.25WHIP and 200+ Ks.
So, while I disagree to have no RPs at all, you can certainly get through your draft with no closers and still be competitive.