In principle, yes.
But it is not the 1943 Westinghouse poster of a "Rosie the Riveter"-like figure captioned "We Can Do It!" by J. Howard Miller that became conflated with "Rosie the Riveter" in postwar years
but the painting by Norman Rockwell from 1943:
The pose in the Rockwell painting does look a lot like the pose Michelangelo chose to display the Prophet Isaiah in in the Sistine Chapel:
(Note that the Norman Rockwell museum once thought Isaiah is the identical to Isaac, since corrected.)
The Russian Wikipedia has a nice description of the paiting:
The composition of the picture literally copies the figure of the prophet Isaiah from the fresco of Michelangelo from the painting of the ceiling of the Sistine Chapel. Although the prophet does not have a box of sandwiches and Red Cross badges, he sits in the same position as a comically-muscular red-haired girl sitting on the background of a wave falling in the American flag, with sandwiches in her hand. On her lap there is a pneumatic gun for riveting and a lunch box with her name “Rosie”, which allows without any signature on the picture to recognize the heroine of the famous song “The Riveter of Rosie”. Her foot tramples a copy of Hitler’s book Mein Kampf, which symbolizes her direct contribution to the victory over the enemy. The lightweight construction of the wire above her head creates the impression of a halo and thereby elevates American girls, who have replaced men in the workplace, to the rank of saints.
The Rockwell museum says explicitly:
Rockwell based the pose to match Michelangelo’s Sistine Chapel ceiling painting of the prophet Isaiah.