No. "Progressive" is, and always has been, a synonym for "communist." To my knowledge, the Republican party has never promoted any communist agenda.
Actually, that's not quite it. A progressive can be in any party - (D), (R) or None of the Above. A hallmark of progressivism is the belief that big (and ever-expanding) government is preferable to small, limited government - and that it does a better job of managing people's lives than the actual people do. Now, the extent to which they believe that varies greatly, from somewhat benign policies to flat-out oppression.
Teddy Roosevelt (R, then Bull Moose) actually started the Progressive movement. Woodrow Wilson picked up the baton and wreaked havoc with it, to the point of resegregating much of the federal government and greatly abusing the Sedition Act of 1918, which he signed into law.
Communism have many intersections with Progressivism, but they are not identical. When Progressivism went out of favor, they renamed themselves Liberals. Hellary reanimated Progressivism when she ran in '08, specifically as an "early 20th-century American Progressive>"
The Left/Right spectrum is actually more accurately redefined as toward or away liberty or tyranny.
After WW2 all communists in the US went by the label progressive. It hasn't really changed since then.