It may work but that would be redundant with the snatches later... also, the 2nd swing day is supposed to be A+A or very similar to the AXE program -- a full 20 min or more of work/rest, whereas the plan you referenced is 5 min.
What you could do is do snatches instead, though -- I might go for 5 OTM. So for instance on Week 8 Session 3, instead of 1H swings for 20 repeats of 10 OTM with your 24 or 28 kg or whatever you might have used for 1H swings, you would do 5 snatches OTM for 20 repeats with your 20 or 24, or even alternate the weight every 2 repeats if you're working up to the 24. Or if you're quite good with the 24 already, use the 28 for repeats. These are building your strength, power, and recovery ability, not so much your conditioning. The conditioning comes with the snatch sessions in week 4, 3, 2, and 1, and you use your snatch size kettlebell for those.