I would advise against trying to harden any axe head to act as a dependable striker - a good striker is HARD, HARD, in the 58-60 Rockwell B range - whereas an axe head should be relatively soft, I like in the mid to upper 40's amybe low 50's on the Rockwell B range at most, so it won't chip out, which an overly hard blade WILL do.
Second I doubt very much if you could get the blade hard enough to work well as a striker since most cast heads are made of failry low carbon steels with only about .40 parts carbon (high carbon steels are generally considered to be about .50 parts and above.)
BTW - scale is NOT formed during the quench - it is formed during the heating and is in good part
carbon, which is why it is so hard (leave a piece of steel too long at too hot in the fire and you'll have pure iron - the carbon will burn off completely). To remove most of the scale one can soak the part in vinegar - much easier than all that grinding, though some may be required.
Also steel in order to bring it to the austenizing point needs to be more in the realm of 1450-1500 and above depending on the type/alloy of steel.
In fact without knowing the type of steel in the head it is tough to suggest the best/correct hardening method as it varies by the type of steel (even every batch of the same steel alloy can vary enough for one to have to tweak their hardening/tempering process for each batch) - this would especially be true if you are a complete novice at workiing steel.
While many of us older smiths enjoy working with "mystery" steel, IMO it is not recommended for the novice, at least not without guidance by some expereinced working with it. One must learn how to do a spark test, how to test for hardness capabilites (harden it and then snap it - something not possible with your head without destroying part of it), whether to use a hot oil quench or a brine quench or a water quench, etc. Without knowing what you're doing you can really mess up - even us old timers with years of experience still get that dreaded PING! a real heartbreaker - Just ask nifeman, Mike Ameling, Wick, Loyd, and other smiths who frequent this site........
My recommendation - polish the head and use as is and then get a GOOD striker from Mike Ameling. I've had one of Pete Allen's cast hawk heads that I've used as a camp axe for better than 35 years and it has worked well in all those years as bought. A quick lick or two with a file or coarse stone and it is good to go.
Can your head be hardened? - yes - but if I were to do it I would harden only the edge - IMNSHO the poll of an axe should NEVER be hardened........
for suggestions on file work - here's some examples that I did based on originals........
as always others mileage will vary.......
afterthought: one possible option for hardening the head - get an experienced smith, somebody like maybe Mike A. or nifeman or ??, to harden it for you properly????