If you're using a PS/2 port that's on your computer, and you remove something from that PS/2 port and plug something else in, you are risking damage to one of the bridge chips on the motherboard (the one that includes the PS/2 interface).
(In traditional PC motherboards this would be the "south bridge" chip. In more modern setups where the north bridge functionality is incorporated into the CPU, it's the "platform controller hub" for Intel, or "Fusion Controller Hub" for AMD. Or in very small platforms it would be in the SOC, "System On a Chip".)
If you unplug the USB keyboard that's going into your converter and plug in a different one, you should be fine.
The problem with hot-plugging and PS/2 is not in the keyboard or mouse but in the PS/2 connector itself. In a connector designed for hot plugging, the contact lengths are staggered so that ground connects first, then power, then the data circuits, and vice versa when unplugging. The PS/2 interface uses a standard mini-DIN connector that was not designed that way. So when you plug in a PS/2 anything, there's a very good chance that the data pins connect before power does, and the result is that the keyboard attempts to draw power through the data interfaces. The line drivers and receivers are just not designed to handle that much current, and they just go poof.
But with an active USB device to PS/2 port adapter you should not have that problem from hot-swapping USB things plugged into the adapter.
On the other hand, what the server will be seeing is the disconnection and connection of a PS/2 keyboard. This won't damage anything but it may not properly detect and initialize the new keyboard. A reboot should cure it.
I have to ask: Why not just use a USB hub?