Yeah, i probably should've
looked it up before going on memory. I just knew we didn't get a top pick by virtue of our season results since going 5-11 in 2000. Here's a smattering of who was picked after BB's 1st-rounders:
2001, pick 6: Richard Seymour (Deuce McAllister, Reggie Wayne, Drew Brees, Chad Johnson)
2002, pick 21: Daniel Graham (Ed Reed, DeShaun Foster, Andre Gurode, Brian Westbrook)
2003, pick 13: Ty Warren (Troy Polamalu, Nnamdi Asomugha, Charles Tillman, Osi Umenyiora)
2004, pick 21: Vince Wilfork (Jason Babin, Karlos Dansby, Chris Snee)
2005, pick 32: Logan Mankins (Michael Roos, Frank Gore, Justin Tuck)
2006, pick 21: Laurence Maroney (DeAngelo Williams, Nick Mangold, Bernard F. Pollard, Greg Jennings)
2007, pick 24: Brandon Meriweather (Eric Weddle, LaMarr Woodley, Kevin Kolb
2008, pick 10: Jerod Mayo (Leodis McKelvin, Joe Flacco, Aqib Talib, Chris Johnson, Matt Forte)
2009, no first-round pick
2010, pick 27: Devin McCourty (Lamarr Houston, Daryl Washington, NaVorro Bowman)
2011, pick 17: Nate Solder (Cameron Jordan, Mark Ingram, Muhammad Wilkerson, Andy Dalton, Richard Sherman) [Ras-I Dowling at #33 was the real mistake]
2012, pick 21: Chandler Jones (okay, a lot of people have been better than him so far)
2013, no first-round pick
I count two misses (Graham and Jones) and a bunch of solid value. Mayo was #10 and is an all-pro, Seymour was #6 and was a borderline HOFer, even picks in the teens (Warren, Solder) have been very solid.
Less tangentially, aside from Jones, basically all of them contributed immediately if I'm not mistaken. Meriweather maybe a bit less IIRC.