Android software to write on anything?
This is definitly possible. There are even multiple approaches I could think of:


Screen mirroring
Some devices already ship with this functionality. My sister e.g. just got her new Samsung Galaxy S4 mini which I helped her to set up, and I noted a related "toggle" in the notification bar to switch "mirroring" on/off. Also, newer builds of the custom ROM cyanogenmod IMHO offer this feature. Especially via HDMI, this also should be supported (maybe requiring an additional app).
Remote Tools
iDev already mentioned Team Viewer in his comment. While the specific component to remote access the Android device itself only exists for few devices (the list might grow, some time given), there are several similar/comparable solutions, as VNC.
Other means
There might also exist specific "whiteboard apps", designed for exactly this purpose. I don't know such one (but I didn't explicitly check for), but searching the Playstore cannot hurt (to ease this, as the "official Google Play website is quite restricted in its search capabilities since its relaunch, I recommend using AppBrain for searching; it's an alternative "web frontend" to Google Play).