Is it possible to launch MS Paint from a link? If so, can I position the program (the way you position a web browser window when opened from a link)?
yes, it's possible to launch from a link, but you can't position it.
You might try IntraLaunch at www.intralaunch.com to easily launch any client-side application. Although I don't think it will let you specify the position, but it will let you open the "On Top".