In what way are you using the word "Yankee"? The two most common definitions are (1) an individual who is usually from the Union states and who opposed the Confederacy during the Civil War, and thus it's a term still commonly used by a southerners loosely to refer to a non-southerner and (2) a New Englander, usually with ancestry in New England going back several generations.
If you are using definition (2), TR IV probably has no New England roots to speak of (other than likely going to Harvard or maybe Yale), so I wouldn't call him a Yankee in that sense. Nevertheless, there have been some New England Republicans beside Coolidge of note who were/are undeniably conservative. Sen. Judd Gregg of New Hampshire today, for one? Or how about John Sununu from NH?
If you are using definition (1), I can assure you that there have always been quite a number of Republicans from outside the South who could hardly be called "some flavor of progressive." Ronald Reagan would be the first to come to mind.
As to TR IV, I've never heard of him. All he might have going for him is his name, and there are hardly any voters still alive who knew his great grandfather other than as a historical figure.