Can a bike have both rim and disc brakes? Was just wondering if a dual option like this was possible or even desirable.
If you are asking one of each type on the bike, yes.  As disc brakes were becoming popular, many companies produces bikes with a disc in the front and a rim brake in the rear.  

If you are asking about one of each type on a single wheel (three or four brakes total for the bike) yes that would also be possible, but there wouldn't really be a point.  Also common during the industry's transition from rim to disc brakes where frames that were designed for either.  Bikes on a manufacturer's less expensive spectrum would have rim brakes and for a few hundred more, the same frame could be had with disc brakes and perhaps nicer components.  

If one was to actually install a disc and rim brake on the same wheel, there would be some obstacles to overcome (assuming you wanted to actuate both brakes with the same lever).  To make the brakes grip roughly the same (ie not one just one doing the work and the other making no contact) you'd have to make sure the actuation ratios or cable pull was the same for both brakes.  After that you'd need to use some sort of BMX style adapter to make sure both were being pulled by the same lever.  You'd also have to carefully adjust them to make sure they making contact at roughly the same time in the pull.  Finally you can expect that since disc pads and rim pads probably don't wear at the same rate, all the work would have to be redone often to keep the two working in unison.  

All in all you'd be paying for twice as brake for a setup that would probably work less consistently than either brake alone and require much more maintenance than either alone.  If you were just wanting more stopping power, you could simply install a larger disc brake (AM or DH sized) and deal with much less setup.

EDIT:  I hadn't considered the possibility of a coaster + rim or disc.  Since a coaster brake would be actuated separately (by pressing back on the pedals) it could be potentially more useful and much less tinkery to maintain.  That being said ANY brake should be able to lock up a wheel so it still won't gain you anything except a safety backup in the case of your primary brake (whichever you chose to use) failed.  

TL;DR Possible, but not worth the effort.