Yeah, not so much. They had really good classes but nowhere near what you stated. Just to make sure the bases are covered, here are Rivals' ranking for what would be the "true" seniors (first number) and fifth-year seniors (second number). Rivals' web site only goes back to 2002 so those are the numbers I included.
2013 - Florida State - #10, #7
2012 - Alabama - #1, #1
2011 - Alabama - #1, #10
2010 - Auburn - #7, #10
2009 - Alabama - #11, #18
2008 - Florida - #15, #10
2007 - LSU - #2, #1
2006 - Florida - #2, #20
2005 - Texas - #1
Also, I'm not so sure recruiting isn't the egg instead of the chicken. That is, I'm not so sure (generally speaking) that you don't get better recruiting classes once you've started having success on the field as opposed to the other way around. Several of the same schools are high in the ranking for a long stretch so it's sometimes hard to tell and you'd have to look at a lot more numbers to be able to tell anything but since Alabama shows up in this list three times, it's an interesting data point. Their first NC on this list had the worst recruiting classes. There second one was better and their third was the best. Correspondingly, they were relatively poor on the field in the early 2000s and started winning when Saban got there and subsequently their recruiting classes got better.