The cap should in no way be a deterrent to using late-round draft picks. The more of them you have, the better your chances of finding guys who will make the team. And every one of those guys who makes the team over a second-year, third-year or even more experienced player saves a lot of cap room -- probably more than the cost of cutting any late-round picks who don't make the team.
AT MOST, the only effect of this being the final capped year (and all accelerations hitting this year's cap) should be that more teams will give their late-round picks three-year contracts instead of four-year deals. That means those players will get smaller bonuses (which means less dead money if they get cut), and they'll be RFAs sooner, with a chance of cashing in sooner if they prove to be capable players.
We have seven draft choices in the final three rounds. Let's say we use all of those picks and sign all of those players to four-year deals, but only three of them make it to opening day -- say, our lowest picks of the fifth, sixth and seventh rounds. The total dead money for the four guys we cut would be about $500,000. But the three guys who made the team would save us about $400,000 if that allowed us to cut guys such as Junior Siavii, Matt Stewart and Courtney Brown. Do you want to give up the chance at getting guys like Jay Ratliff, Patrick Crayton, Orlando Scandrick or even Jacques Reeves just to save a possible $100,000 of cap room? If just one more of those late-round picks this year made the team over a third-year player, we'd be saving more cap room than we'd lose in dead money. Or, if all three of our fifth-round picks made the team but we cut all four of our sixth- and seventh-rounders, we'd still be saving cap room.
Remember, SOMEBODY will be taking up the last half-dozen or so roster spots on the team. Would you rather have them be costlier, mediocre veterans, or cheap rookies who can do the job just about as well but could become even better?