Welcome!
Yes, Inkscape can put text on any kind of curve. Here's the manual info on that:
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Text-Path.htmlI'm not sure if all the fonts that you see in Word are available in Inkscape. Inkscape requires that fonts are installed on the operating system, to be available. I'm just not sure if Word has the same requirement, or if Word can use fonts that aren't installed (apparently some programs can, and on some operating systems). There's currently a bit of a bug with Windows 10 and fonts, which we can help, if you run into it. But you didn't mention your operating system.
Although I guess Word is a clue

If you have some installed fonts that you don't see in Inkscape, let us know, and we'll explain.
Inkscape is free and open source. It installs fairly quickly and easily. (On Windows, the first start might take a few minutes. As far as I understand, the delay is caused by caching the fonts for the first time. But just give it a few minutes.) So you can open it up and have a look at the font list. Then just uninstall if you don't like what you see. You could even get the 7z package, and it wouldn't even be technically installed.
Inkscape has sort of a flowchart tool called the Connector tool. But it seems to be a little buggy to me, and I would avoid it. You can use the regular path tools (Pen/Bezier or Pencil/Freehand) instead. (Although that's just me, and you might not have the same experience.)