That is a very old version of Kubernetes so you will probably find some problems & be very much on your own - I’d expect HashiCorp probably will limit their level of support if you did go Enterprise (as you wouldn’t be able to use the standard Helm chart, etc.)
With regards to it actually “working” it depends on what you are trying to do. If you just want Vault with K/V and AppRole it would probably work - with the proviso that you’d need to sort out the deployment yourself.
If you wanted to use anything more integrated into Kubernetes, such as the Kubernetes auth engine or the Vault pod injector you are more likely to be out of luck. They actually talk to various Kubernetes APIs so quite possibly will need APIs that might not be available that old.
Especially as Vault is security focussed I would be very reluctant to be running it on a version of Kubernetes which is not supported and has known security issues.