Is it possible to represent text within an svg document as if inside (an invisible) textbox? Such that the text wraps onto the next line when it hits the end of the box? I looked at the svg specification, but I couldn't see a way to do this.

It's not possible in SVG 1.0/1.1. But the SVG Tiny 1.2 Candidate Recommendation includes this feature (using a 'textArea' element).

You can still use Inkscape's feature Flow into Frame, where frame is any closed path. When you like the way it looks convert text to paths and you can save it as plain svg.

you dont have to convert to paths, you can do convert to text and it converts it to lines of normal text.