Yup:
2013: +Buchanan, -Beauharnais. Unless you count that 7th traded for Blount.
2012: +Dennard, +Ebner, -Ebert.
2011: -Markell Carter, -Malcolm Williams. Also -Lee Smith, taken in the 5th round.
2010: +Brandon Deaderick, -Kade Weston, -Zac Robinson, -Thomas Welch (traded 2 7ths to move up for him), -Ted Larsen (should have stuck, though - that was a mild mistake)
2009: +Julian Edelman, +Myron Pryor, -Jake Ingram, -Darryl Richard
And then there was 2007: -Oscar Lua, -Mike Richardson, -Justice Hairston, -Mike Elgin, -Corey Hilliard, -Justin Rogers. 0 for 6.
Probably not far off from the league average. 6th and 7th round picks are really pretty much equivalent to UDFAs, just the teams get to lock up their rights instead of trying to sign them on the open market. Almost every team cuts late round picks, and almost every team has UDFAs that make the 53 man roster.