When you delete a file in Laserfiche, is the physical space on the hard drive immediately available for utilization for a new file to be written there?
The file on the volume isn't deleted immediately, it's done as a background job by the Laserfiche server. As soon as the file is deleted the space it used to take up is available to store other data.
you must defrag the Hard Drive before this empty space (he called it White Space) is usable
This is not true. A defragmentation process rearranges the way a disk's storage is used so that the blocks that hold the data for a particular file are brought closer together, and blocks that are not currently allocated to a file are all together. The main purpose of this is to reduce the amount of seeking that a disk head has to do to read the data of a particular file - it's more efficient to read consecutive blocks than it is to seek around the disk. Since it's just moving things around, there isn't any more usable space after the process than before.
SSDs work differently from spindle disks and essentially don't seek, which is why you don't defrag them. Defragging requires low-level access to the disk, so you can't do it on systems like a SAN - at least not the same way you can on an attached hard drive. If you have one of those, consult the documentation.