Once you drill past 5xdiameter you are in deep drilling..
To drill an axle you are around 18 times diameter with say a 10 mm hole.. , half of that if you go from each end.
Gundrills are for deep holes in production, and tend to have coolant pumped thru them...be sure yet quickest way if you were doing a lot of them.
I would be far less worried about drilling an axle with a reasonable size hole, in unknown material....than I would be about trying to heat treat an unknown material..