I've tried it, and a really sharp mirror edge will slice a tomato like there's no tomorrow. But, as Chalby said, as soon as you lose that hair-whittling bite, the polished edge will skate.Give it a try, sharpen a kitchen knife down to about 2000 grit, this is where I like my kitchen knives with a bit of toothiness, and it will slice ripe tomatoes with ease. Then sharpen that same knife up to 8 - 12,000 grit and strop on 0.25 mic paste, this will shave like no tomorrow, slit hairs etc, but will struggle on a tomato.
The skin on the tomato, especially cherry tomatoes are rubbery and smooth and require that bit of toothiness to initially tear the skin to start the cut.
FWIW, I don't consider 2000 grit to be a toothy edge. To me, toothy is an edge in the 300-500 grit range.