There's probably some official academic definition for multitasking, but I'm not really sure what it is ... I think that's going to cause a lot of disagreement and confusion in this thread, but I'll take a stab anyway.
When my students use the term "multitasking," they seem to mean two or more completely unrelated activities, each of which would require full conscious attention, and yet somehow performed simultaneously. Like when they say "I can listen to your lecture and text my cousin at the same time!" Um, no. I'm pretty sure the brain doesn't work that way. What they're really doing is switching their attention back and forth, and missing out on one while they think of the other.
I think that's different than a complex activity that can involve a lot of different things but are still related as a whole. I'd say piano is more like that. I've heard good pianists say that it's not like using two hands with five fingers each so much as one big hand with ten fingers. š Just like when I play guitar, my left hand chunks the movements of the individual fingers into chord shapes rather than thinking of putting down each finger individually.
As someone who sings and plays, I'd say that all still works as one complex activity: just like practicing hands separately and then putting them together, my voice is just one more "hand." Other things can probably be added to that too: pedaling, general performance motions and expressions, etc.
There are some times when I do have to multitask a bit though. Using various foot controls on my synth to change programs on the fly is an example. Psychologically (for me, anyway), those always feel like separate things from playing, so I have to put my playing on autopilot / muscle memory for a minute while I mess around with the other stuff.