It is possible to approximate text following a curve by using separate text-only shapes for each word.
Many people ask if it's possible to put the baseline of text on a curve in Visio.
As you just learned, text for a shape is contained within a text block. The keyword here is block — a rectangular area that the text is confined to. Unfortunately the base of the block cannot be sculpted or morphed into a curve.
Given that text blocks are always block-like, continuous text on a curve is not a quick and easy task in Visio. But you can approximate this with a little extra work.
Just make separate text-only shapes for each word, and then rotate each word so that they appear to follow the curve. Some words may be too long, in which case you might have to modify the curve or make separate text-only shapes for each letter in that word.