Would there a be a significant security/privacy advantage to running a .onion site in a VM that lives entirely on a ramdisk?
RAMdisk means in RAM not on media. That devolves to cold boot, or even FDE, attacks, both of which are relatively harder or complicated or short time window than plaintext disk. Or process and general memory space and I/O capture in real time by VM parent, hypervisor, etc.
If you can't trust the VM parent, which you probably can't, the answer might be no, or yes, depending on the range of capability estimate you assign to them.
dumped in the event of an emergency
Some OS have knobs to turn off all swap, dump, pagefiles, etc that otherwise go to media by default.
Your questions are far too generic so no one can really help you.
Sit down and chart out your own datasets, risks, threats, backups, etc. Punch your questions into any search engine. Learn OS admin as needed. Etc.