I suspect so, if you use a decent blade and take it slow, drill a hole big enough for the blade inside the cut out area, then work the jigsaw out to the line (if you do it right, you end up with the blade following the line as it meets it).
If you had a Router, that could possibly do it very easily, as many have a trammel bit that lets you anchor them to let you do circles easily as it sets the distance away from the centre the router works (so you just take the route round a few times at increasing depths).
Remember to wear some old clothes (or a boiler suit/apron), googles and mask.
And do it either in the Garage, or outside, as MDF dust isn't very nice, and makes a heck of a mess.
Will the holes be visible?
As if not, it doesn't need to be quite so neat and tidy which makes things easier
