I've made soap with full-fat milk and I've made soap with about 17% of the fat coming from cow's butter. I don't pick up any odor from the milk soap, but there is a distinctive odor from the butter-based soap. A soap made from high fat cream could also have this odor, depending on the amount used.
I think "vomit" is a little strong, but it ~is~ an unusual cheesy, yeasty kind of odor. It fades with time to a faint tang, but doesn't entirely disappear. If you soap with a high % of butterfat, you'll want to scent the soap accordingly. I think I'd go with spicy or woodsy scents. The mint EO I used was ... okay. Florals would probably be a bust.
The other issue with a high % of butterfat in soap is that soap high in butter may be as or more more irritating to the skin than the same % of coconut oil in a soap. This irritation factor is due to the short-chain fatty acids in butterfat -- specifically the 4-carbon butyric acid that Irish Lass mentioned as well as a dab of 6-carbon caproic acid.
Soapcalc does not consider fatty acids shorter than 12-carbon lauric acid, so it won't give you any indication about this issue. For that matter, since coconut oil, palm kernel, and babassu all contain 8-carbon caprylic and 10-carbon capric acids that are also known to cause skin irritation, Soapcalc doesn't tell you the full story on these fats either. The shorter the fatty acid, the greater the tendency to cause irritation. The main culprits for irritation are 12-carbon lauric acid and the shorter fatty acids.
Be sure to calculate the recipe based on the actual butterfat content of the butter. Butter isn't 100% fat.
I don't think there is any particular issue with rancidity. I made a batch of the 17% butterfat soap without EDTA, and the bar I kept in my stash for several years never had any issues.