In the BB era, here's all their 7th round picks:
2000: Casey Tisdale (nothing), Patrick Pass (solid player for a handful of years)
2001: Owen Poachman (nothing), TJ Turner (nothing)
2002: Antwoine Womack (nothing), David Givens (good player who helped win a couple of SBs)
2003: Spencer Nead (nothing), Ethan Kelley (nothing), Tully Banta-Cain (helpful player who did well for them for years)
2004: Christian Morton (nothing)
2005: Andy Stokes (nothing), Matt Cassel (hugely helpful player in 2008 and got some good trade value when they moved him)
2006: Willie Andrews (2 years of special teams play)
2007: Oscar Lua (nothing), Mike Elgin (nothing)
2008: no 7th rounders
2009: Darryl Richard (nothing), Julian Edelman (future Pats' HOFer)
2010: Thomas Welch (nothing), Kade Weston (nothing), Zac Robinson (nothing), Brandon Deaderick (useful player for 3 years for NE)
2011: Malcolm Williams (nothing)
2012: Alfonzo Dennard (played 3 years for them, good ST player), Jeremy Ebert (nothing)
2013: Michael Buchanan (not much), Steve Beauharnis (nothing)
2014: Jeremy Gallon (nothing)
2015: Xzavier ****son (nothing), Darryl Roberts (didn't play for NE but had a 6 year NFL career)
2016: Devin Lucien (nothing)
2017: no 7th rounders
2018: Danny Etling (nothing), Ryan Izzo (nothing), Deion Crossen (not much for NE but has had a 5 year NFL career)
2019: Ken Webster (nothing)
2020: Dustin Woodard (nothing)
2021: Tre Nixon (nothing, but stayed on the PS for a while and may land somewhere)
2022: Andrew Stueber (seems to be nothing)
2023: Isaiah Bolden (who knows, but he has potential)
So that's 38 7th round picks in the BB era. Of those:
1 (2.6%) superstar (Edelman)
1 (2.6%) really good player for NE (givens)
2 (5.2%) solid players for NE (Pass, Banta-Cain)
3 (7.9%) useful guys for NE (Cassel, Deaderick, Dennard)
2 (2.6%) guys that did nothing for NE but have stuck in the league for a bit (Crossen, Roberts)
29 (76.3%) players that effectively have done nothing in the league
9 (23.7%) players that have been legit NFL contributors or better
I'd say that basically a 1 in 4 hit rate with your 7th rounders is pretty solid actually.