The shape of this draft is weird: we've yet to see the 1st round pick on the field, we hope not to see the good-looking 2nd round pick for the rest of the season, and they didn't pick in the 3rd. So the weak crop of 6th and 7th rounders stands out more than it should. In reality, they're very much the norm -- the team (like all teams) typically only hits on one late-round pick a year, despite drafting as many as 5 players in rounds 6 & 7.
In fact, the only time in the last decade they've hit on more than 1 is 2012 with Dennard and Ebner. (Unless you count Myron Pryor as a hit in the 2009 class of Pryor, Ingram, Edelman and Richard).
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.