Some do, some don't. Increasing numbers of them have touchscreens though. Also, some of them have access to the Android Play store, so if it can be packaged as an Android app, that might also work. I don't know what sort of API's chromebooks have for pens though.

Alternately as a web-app, but again, not sure what APIs you have access to - I recall there being a stylus web-api about 10 years ago, created by wacom, but it died.

Many do but not all (I have a Samsung which does and an Acer which doesn't).