Supporting Les.
The chances of it being through hardened is remote, but it may well be toughened which is worse almost.
To be honest, one has to ask whether its worth doing. The cost of a purpose made one is not great, and very cheap given the awkwardness of holding the job, and possibly knocking the end off a tip.
Unlike Les i do like a drawbar-ed chuck in a mill or lathe, just to stop any work from causing it to spin after a grab, or from being shaken about in thin metal.
So I’d keep using it for drilling, having ordered the replacement, and then swap the chuck over.