Doc Green
I just gave it a try. Ripped a 3/4" square blank off a poplar board, 24" long. Mounted it between centers, then installed it between a chuck and point center.

My first thought: Wow, that is Long! Made an attempt to turn it to a dowel 1/2" in diameter ... to impress John. Didn't work.

When I got the diameter down to about 5/8", the whipping became severe near the center of the piece. I tried a gouge in a traditional cut, a gouge as a shear scraper, a round-nose scraper in the shear-scraping mode, and a skew. Each tool produced a similar result: whipping that gave rise to a rough, spiral pattern near the center of the blank.

I had no problem as long as I was working only 6 to 8" from either end of the blank.

Even though I was trying to take the diameter down to less than 3/4", I now believe that a small steady rest will be required to prevent the whipping, even for a 3/4" dowel. That is, treat the dowel as if it were a trembleur.

I was not able to prevent the whipping by holding my hand/fingers against the piece.

Live and learn. ~Doc