I wrote an elaborate post, but I don't believe it's worth inclusion... a modified bsd.rd kernel exists for OpenBSD that includes an OpenSSH daemon, but that alone will not allow you to install an OS on the system.
http://erdelynet.com/category/tech/yaifo/
You need to be sure it's a real system, not a emulated or "Virtual Private Server", and you
require permission from the people you're leasing from.
It's possible, I'm not going to lie... but you would need to prepare a disk image with the above custom kernel and write it directly to your servers hard drive, but if you accidentally make a mistake, you won't be able to fix it.