Can one use butter to replace cream or milk in drinks?
No, it won't help you at all. Butter won't mix with any drink short of vla*. You will end up with a cup of coffee with a puddle of greasy melted butter swimming on top, or a chunk of butter if you are using iced coffee.

I've read questions on here that there is limited success mixing buttermilk and butter to get cream

The only question I have seen here which claims successful mixing uses milk (not buttermilk) and butter, emulsified with a vintage hand-operated device. If you had the device, there would still be two big problems left:

it is made for milk + butter, not water + butter
having the emulsion be stable under heating is quite a requirement - after all, even real cream separates in coffee if it has been standing around several days (if yours doesn't, it probably has added carrageenan).

And if you find out that it works nevertheless - are you really prepared to search for that kind of device on second-hand markets, have it take up space in your kitchen cabinets, and then, just when you are frustrated because your morning coffee is brewed but you have no cream, spend half an hour cranking?
If I were you, I would store a few sachets of powdered non-dairy creamer.
* I am now expecting a number of comments listing drinks which will mix with butter after all. My hunch is that none of them will be the kind of drink to which people add milk after serving.