YES-----Almost!
A 16F84 and most computers can only do one program at a time. Your PC may look like it is working on many programs but it is only working on one at a time.
I have a PIC16Fxxx running a program most of the time. Every 0.01 seconds the computer jumps to an interrupt program. It runs for about 0.001 seconds then goes back to the main program. To the human eye it appears that both programs are running at the same time.
Generally you can do what you want in this sort of thing, but it's far better to be specific - you could write a real time multitasking OS, but you absolutely cripple performance, as Windows does!.
I suggest you ask us exactly what you're trying to do!.
You can also get some sample chips from microchip for free. That goes for antique chips to the really fancy chips. For programming, on top of learning on some hardware characteristics from sample code and datasheets, may be helpful to look at structures of c programs as well or assembly.