Can the oil become rancid like cooking oil?
It can and does. This is a known and common drawback of emulsified cutting fluids, they quickly stink and could be unhealthy. I ignore if the proportion is of any help.
At least in one workshop I used, we made the emulsion ourselves. I suppose, but am not sure, that the "oil" was already an emulsion because water addition went very quickly and easily: just mix and vaguely stir. Or it contained an extremely efficient emulsifier, magic to me.
So delayed water addition is already solved somehow. Avoiding rotting would be useful. Research has already been made, progress would be welcome.