Are we talking physical servers like Poweredge or Proliant? Those take a long time to boot, especially with lots of RAM. Why can't you use suspend/resume?
And modern servers don't really consume a lot of power while idle. You can configure them to downclock the CPU and GPU while idle just like a desktop or laptop.
But if you really wanted it, you could boot an immutable distro and mount user partitions tmpfs. Or use a portable distro and discard the state. Or a filesystem with snapshots and roll back on each shutdown or boot. But none of those are really going to get you instant boot. Linux boots pretty quick, but not instant.