Has a point guard ever averaged 1 block a game?

Not since blocks became a recorded stat in 1973-74.

Basketball Reference does not allow querying specifically for point guards as opposed to shooting guards, but very few guards of any kind meet your criteria of 1+ blocks over 70+ games. This is the entire list:

Player             Season   Team  G  Minutes Blocks
Michael Jordan     1987-88  CHI   82  40.4  1.6
Michael Jordan     1986-87  CHI   82  40.0  1.5
Dwyane Wade        2008-09  MIA   79  38.6  1.3
George Gervin      1977-78  SAS   82  34.8  1.3
George Gervin      1976-77  SAS   82  33.0  1.3
Reggie Lewis       1991-92  BOS   82  37.4  1.3
David Thompson     1977-78  DEN   80  37.8  1.2
Dennis Johnson     1978-79  SEA   80  34.0  1.2
Dwyane Wade        2009-10  MIA   77  36.3  1.1
Vince Carter       2000-01  TOR   75  39.7  1.1
Dwyane Wade        2010-11  MIA   76  37.1  1.1
Vince Carter       1999-00  TOR   82  38.1  1.1
George Gervin      1978-79  SAS   80  36.1  1.1
Dwyane Wade        2004-05  MIA   77  38.6  1.1
David Thompson     1978-79  DEN   76  35.1  1.1
Danny Green        2014-15  SAS   81  28.5  1.1
Reggie Lewis       1990-91  BOS   79  36.4  1.1
Jerry Stackhouse   1995-96  PHI   72  37.5  1.1
Michael Jordan     1990-91  CHI   82  37.0  1.0
George Gervin      1979-80  SAS   78  37.6  1.0
Dennis Johnson     1979-80  SEA   81  36.3  1.0
Ron Harper         1986-87  CLE   82  37.4  1.0

^{Provided by Basketball-Reference.com: View Original Table. Generated 12/23/2016.}

Ten different players appear in the list:

• Michael Jordan - always a shooting guard
• Dwyane Wade - was listed as PG only during his rookie season (2003-04)
• George Gervin, Reggie Lewis, David Thompson, Vince Carter, Jerry Stackhouse - all SG/small forward combos
• Dennis Johnson - was listed as PG for about half of his career, but his first PG season was the year after his last 1+ block season
• Danny Green - SG
• Ron Harper - began as a SG and finished his career as a PG, but his first PG season was ten years after his 1+ block season

None were listed as point guard during their qualifying seasons.

In the 2016-17 season Andre Roberson is the only guard averaging 1.0 blocks per game, but he, like most players on this list, has never played PG.