Machining O-1 drill rod

Yes.
It would be much easier.

O-1 drill rod will work just fine

Drill rod is "tool steel" in that it is suitable for making into cutting tools. Drill rod as it comes from the supplier is in the annealed state; that is to say it hasn't been hardened and is machineable with standard cutting tools. After machining you can harden it into tool steel, if desired. In some cases not intended for cutting or subject to heavy wear, such as your expanding mandrel, it can be left in the annealed state. Modern tool steel (O-1 or W-1) is generally considered to be high carbon tool steel by definition as opposed to HSS (High Speed Steel) which is usu. used for making drill bits and other cutting tools. A major difference is that HSS can't be heat treated in the home shop without special equipment.
Bob Swinney

That's the wrong grade of carbide for steel. Choose a C5 or C6 grade. C2 is excellent for non-ferrous and stainless. (Yep, stainless!. Also very good for cast iron).
Drill rod is tough to cut, but actually cuts quite well (clean, not like 1018, that likes to tear).. Take light cuts with moderate feeds and you should do fine. Use a little cutting oil to keep the chip welding to a minimum. You might also consider using HSS instead of carbide. It does a much nicer job of turning tough materials on small machines. If you can grind a small chip breaker that forms a positive rake, you'd have the best of all worlds.
Not for a tool, you wouldn't. You'll get better service life from the drill rod, but if you intend to use it once or twice and never use it again, the leaded stock would be much easier to machine, and would hold up fine for limited use.
Harold