Hi Tom,
I feel for ya on this one. Management always seems to look at these situations as wasting money when you start tossing out electrodes, when they should have been properly storing/maintaining the inventory to start with.

With me, I got to hear about how "I" wasted thousands of dollars worth of A325 and A490 high strength TC bolts when I tossed out the seemingly good bolts that didn't have any traceability, and these are the bolts that were bought and shipped directly to the jobsite and were not used, then returned to our shop at the end of the job. Open kegs, some with water still standing in them, other drained of the water by someone punching holes along the bottom of the kegs, some in fairly good shape visibly but lacked any paper backing for the files. The fun never ends and the parties responsible for the wasted dollars (that came off of our bottom line that determines whether or not I get a Christmas bonus or not) goes unidentified and unresponsible for their mess.

Your right, it does require proper marking, and maybe my original response was not clear, so I will clarify it now.
Look at it this way.
What does it take for a company to affix that proper marking? After the rod is burned, What documentation
is reviewed. The rod is long gone, how do you document what material was used, and
that it was compatible and right with the base material specified?
I may be wrong here, but for traceability, it's an entire system, not just the welder checking to see if the rod is marked
properly. I can mark a coat hanger wire with legitimate looking markings, but does that make it a documented filler material?
Now maybe I'm wrong, but there is a reason the codes require marking.

In D1.1 for instance:
3.3 Base Metal/Filler Metal
Combinations
Only base metals and filler metals listed in Table 3.1
may be used in prequalified WPSs. (For the qualification
of listed base metals and filler metals, and for base
metals and filler metals not listed in Table 3.1, see
4.1.1.)

This requirement goes to the listed filler materials such as A5.5, but as most know,
it just doesn't end there. Under A5.5 the following references are listed as
Normative.
Excerpt from A5.5
"2. Normative References
2.1 The following standards contain provisions that,
through reference in this text, constitute provisions of
this AWS standard."

This means that A5.5 as is the mirrored versions of this in other standards
do not stand alone, but rather are intend and required to be used with
the normative standards of which the following are included for A5.5

AWS 5.01 filler metal procurement guide
AWS A4.3 standard methods for determination of the diffusible hydrogen content of martensitic, bainitic, and ferritic steel weld metal produced by arc welding
AWS A4.4M standard procedures for determination of moisture content of welding fluxes and welding electrode flux coverings
AWS B4.0/M standard methods for mechanical testing of welds.

There are other relevant direct specs listed, ISO 544 for instance. "welding consumables-technical delivery conditions for welding filler metals, types of product, dimensions, tolerances, markings"

A5.01 is in that same realm, and both indirectly and directly other API Navsea and others are listed. 

Without getting overly anal, that marking isn't just some company painting numbers on a rod, there is a whole host of requirements for that marking to be legitimate and traceable.

As with most things, the devil is in the details.

Under 5.5

3. Classification

a list of requirements are given, one of which is chemical composition of the weld metal and a reference to Table 2.0

Under Table 2.0 is listed as "CHemical Composition Requirements for Weld Metal"

Thats a clear statement that the weld metal should be within the listed requirements.
That leaves the question of how do you assure and document that?

Which kicks you back to documents such as AWS 5.01 and ISO 544 and others as listed in the normative reference section.

Going to AWS 5.01

Underneath 4.1 of 5.01 the following excerpt
"For identification purposes.. each manufacturer assigns a unique designation to each quanity (in reference ot heats, lots, blends, batches, and mixes) This designation usually consist of a series of numbers or letter which will enable the manufacture to determine the date and time of manufacture, the type and source of the raw materials used, and the details of the procedures employed in producing the filler material"

Then comes a key statement
"This designation stays with the filler metal and can be used to identify the material later, in thoses cases in which identification is necessary."

There in is a little more detail as to why the ""MARKINGS" are required.

To summerize, when the markings are required, as most codes specify, then the traceability is by default required, and hence the requirements for traceability in general. (including heat)

As a post script, The quality assurance plan of the company in question should address all these matters.
But as listed in the previous post, if an auditor, inspector, AI ect wanted to be anal, or if your sued
for a failure or other mishap (most especially the later) A weld shop can be brought to task on that issue.
If a lawyer ask you as the QA manager "How do you know it was the right material" telling him "well
the rods had the right markings" will be found as patently insufficient as an answer.

hogan,
D1.5 I am completely unfamiliar with.