I'm not a fan of it. Getting one point in a category is hard to recover from, even if you all out win Ks and Wins. You're also most likely taking a hit to your ratios, which means you have to make up even more ground with your offense. It's doable, but I don't think it's worth it. I think it's easier to build a more well-rounded team than it is to make up for punting a category.
example: You should be aiming to get around 100 points to win a 12 team league. That means around 10 points in each category. If you punt saves, but all out win Ks and wins, you still still need to gain an extra point in every offensive category to make up for that, and that's not even taking into account possible points lost in ERA and WHIP. I personally don't think that the benefit of not having to draft two closers is going to make that kind of boost easy.
Unless they are super bad, relievers barely affect ERA/WHIP because they pitch so few innings.
The idea behind punting saves is that while others are using picks on closers, you are grabbing a better player. You can get good saves late in the draft so you probably wont be getting studs in lieu of those punted saves. If you usually grab top closers earlier in the draft, then its another story.
Other thoughts -You can "punt" saves on draft day & grab closers off the wire due to injury or closer changes -Two high K relievers = 1 ace SP w/o the wins.
I usually employ this as a strategy only if necessary as the season progresses not as one at the beginning in a draft. As others have noted, punting a category like saves usually leads to degraded ratios so it takes down 2 other categories as well unless you are really fortunate and step into an uber staff late in the draft or on the wire early in the season. It is better to target mid-tier closers and scrounge a closer out on the wire so as to try to at least get 5 points out of the category imo.
That said, sometimes stuff happens and your closers get hurt, lose their job and\or outright stink up the joint and you get buried in the category in the first 2 or 3 months. That is when you re-valuate your team and maybe decide to load up on starters and push for Ws and Ks rotating in reserves and\or trading for extra starting pitching. Sometimes I laugh when I see an owner who is like 9th in saves and about 20 behind the 8th place team mid-season trade a top bat or starter for a closer...for what?...He will be lucky to move up 1 point. Bag the category and trade for starters. It is easier to say than do sometimes obviously.
Unless they are super bad, relievers barely affect ERA/WHIP because they pitch so few innings.
Or if they are super elite. A RP who posts a 1.50 ERA and 0.90 WHIP makes a pretty large impact on your ERA and WHIP even with only 60 innings. Certainly enough to gain a couple of points in each category.
I'm not a fan of punting in roto. As another poster elaborated upon, the 1 point in the saves category is extremely difficult to overcome. In H2H, I have no problem punting, but saves is another tough one to punt since you will also take a small beating in ERA and WHIP. You would have to be prepared to stream pitchers on a daily basis if one of your SP has a bad outing to overcome the ERA and WHIP hit.
However, all is not lost:
The reason one punts a category is to take the most value in the earlier rounds. If you punt SB, Mike Trout is no longer a top ten option. So the reason you punt saves is to reduce the number of high draft picks "wasted" on closers. Why not wait until the end of the draft? Your last 3 picks and take middle relievers with a clearer shot at making the closer role?
I have employed this strategy, along with being aggressive in free agency, in one of my leagues and consistently rank in the top 4-6 range. I still get the positive effect in the draft and not the 1 in the category.