it'll work (any grease is better than no grease) but auto grease is probably a tad on the heavy/thick side... I'm sure Chris King has a really expensive grease they sell but I'd guess any decent bike grease would be fine.
It took much wrangling, but CK finally came thru with the specs of the grease that is stock in their BB bearings: NLGI type 2.
NLGI type 2 is used in more auto applications than any other so you have lots of choices. If you decide to go with any other spec grease you must get rid of all of the original grease or you can have total lube failure.
For a NLGI type 2 grease I like Valvoline DuraBlend Synthetic Blend Grease part #VV279. Good stuff, it is loaded with moly.