I can't find much about using fleurons/hedera as bullets in a list online or in Bringhurst, but I did find several "floral heart bullets" in Unicode. Are these still only for decorative use? Would their use in a complex list be a faux pas?
As with most things, there is no hard and fast rule. My only advice would be this:
Those are fairly complex and intricate, as opposed to bullets which are usually very plain and simple - just a circle or a square. Thus you don't want them to be too distracting. If the information is important (like in a technical manual, to take an extreme example) then I wouldn't use them. But if they are in a context that calls for more decoration such as an invitation, and they aren't overused (no long lists over 2 or 3 items) then that might be ok if it looks good, and you have plenty of white space in your design so it's not too "busy".
You might also consider pairing them with a more simple font rather than a highly decorative or stylish one. But again, just a suggestion. There is no hard rule.