I just changed out my cassette and chain. I have a bunch of gunk at the back axle (grease from when I bought the bike, probably), but when I was changing out the cassette I didn't have a good place to sort the parts (or the replacement grease) to re-grease the hub. Will I really be doing myself that much of a favor to take the bike apart and do it right or do I really need to think about it?
I smirk... only because it's a one-in-all-in call, or you leave it alone. You choose!
Actually, if the wheel is spinning smoothly for 15+ revolutions after a good hoik and without any grinding noises, and there is no lateral movement in the wheel at the when you try to move it in and out at the tyre... it's probably best to leave well enough alone. Just clean away the gunk with a clean rag, but avoid pressing the old grease back into the hub (the black gunk indicates the hub was probably overloaded with grease in the first place...)
However, if you are inquisitive, have cone spanners in particular, have a work bench or table so you don't lose errant bearings in thick-pile carpet, can clean up the balls, races and cones, apply new grease, and can preload the bearings just right to suit the quick release or nutted axle you have... by all means learn.
There's plenty of advice here should you have further questions.