Yeah, that is another way to do it actually. Once the rod is in the chuck, you could even drill a hold through both the chuck and the rod and fit a bolt or pin of some sort to stop the rod from slipping or coming loose.

If I remember rightly, the reason I didn't do this was because the diameter of the rod was too big for the chuck. Most cheap cordless drill chucks have a capacity of 10mm diameter and my piece of threaded rod was 12mm diameter. Not a problem if you have a lathe and can turn a section of it down to fit, but I didn't and I found that my home brew method of decreasing the diameter by trimming with an angle grinder wasn't accurate enough (off-centre cutting led to rod wobble when it was spinning)

There are probably some smaller jacks out there that will have a smaller diameter threaded rod though, which should work fine if the chuck method is your favoured form of attachment.