Yes. But for all practical purposes, no.
True it's not the sort of thing most computer users would do since you need
third-party software to engage the format subroutine in the drive's
firmware. Google hard-disk recovery tools and you'll easily find something
with that feature.
"Low level formatting" involves writing track/sector data to the drive
along with other data and a byte pattern. It was normally done (via
DOS) with 5 1/4" floppies, maybe with the little floppies too, but
took a long time even when disk capacity was 80 KB. Given the size of
hard drives it would take bloody forever now even allowing for the
vastly greater CPU and drive speed.
However, it *could* be done if one knew what one was doing, had a
program to do so (or could write one directly accessing the disk drive
controller) and had eons to wait.
There are a bunch of utilites out there that will let you send the format
command to the drive. I did it a few times several years ago and got mixed
results. Some drives seem to implement it as a no-op while others take
gobs of time doing something to the platters. I assume it is as you said
that a pattern is written to the drive including a gap on each track of
known length and other data which is going to be particular to the software
running on the drive's controller board.
I suppose there are good reasons as to why it generally takes so long to do
the low-level format, but it's not clear that it would take proportionately
longer on hard-disks of contemporary size since they are also so much
faster than earlier models. To wit, in my laptop I have a tiny little
Fujitsu 120G drive that sustains 40MB per second. That's just crazy in
comparison to what I could get out of a fast Seagate drive ten years ago.
Progress is your friend.
If low-level formatting doesn't seem to do anything, you'll just have to
live with the fact that hard-drives (yours included) are closed systems
without user-serviceable parts inside.
Dr. Beard