Assembly lube is generally high in ZDDP, although not necessarily. there is no legal description. #0 grease is the same as #2 but with less thickener.
In general, it is a bad idea. Exceptions to all rules, like when there are bad seals, but you will have less cooling, less settling of any debris, more emulsification of any moisture, etc.
I do recommend a light grease in steering boxes that once called for heavy oil. Cooling isn't an issue there, nor speed to throw off the grease.