Yes. It is possible to install press in all servers that provide External and Internal IPs.
But let me remind you, Frappe uses AWS and their Frappe cloud / press app is designed to handle all server activities within Frappe Press without ever leaving the press app.
For example see this:
You can create, stop, start, resize disk sizes all from Frappe Press. But I think this is possible only with AWS (as far as I know, actually I have not tried with any other provider).
Checking the cluster doctype, I can guess that this feature is available for Hetzner and Oracle as well. (need to verify the extent to which this support is provided)
So, you can only confirm by trying yourself. But I believe if you use press at above mentioned commit (see Edit 1 in post), you should be able to install Press in any server you want.