As far as I know, "hot plug" means that if the drive/cables/bios are all capable of "hot plug" then the following should happen.
If the sata cable has a "hot plug" connector (slightly shorter connections on some of the pins) then the drive should perform a clean shut down. (clear the cache by writing the data to the drive, then powering down)
The PC should report to the OS that a drive has been removed. (without hot plug it might send; drive failed, link failed, or might not report anything and will leave it up to the OS to "do something" if/when it next tries to access the disk.)
The OS (or raid card) should then handle the "drive removed" in the best possible way. (without hot plug it might try; resetting the drive, resetting the link, or it might keep retrying the drive to see if it will come back up.)
Its down to the OS to decide if/how it presents "eject/safe remove." The default standard is to have such an option for non-directly connected drives (esata/usb/etc.) and no such option for direct connected drives as its assumed they won't be "pulled" unless they have failed (sata/scsi/sas/raid card).
I have seen third party software on non intel servers where it was possible to "eject" an "internal" hard drive where the physical drives were in hot swap caddies prior to pulling them, but the assumption is if its "internal" then you really should shut down before rooting about and pulling drives as its all to easy to pull the wrong one or knock a loose cable.