The problem is soreness. You have to find a way to balance S&S and the pressing training. I've without trying to use any special planning or science aimed to develop both S&S and kettlebell pressing together. I found I just needed to be sensitive to not overdoing it.
Overall, what I discovered for myself about myself is that I could manage around 2-3 sets of military presses around 2-3 times a week (remember that how many reps is more variable and of course tend to go up in time before you jump up to a heavier kettlebell) and my pressing weight went up. It likely has as much to do with technique and movement-pattern training as it has to do with actual strength, as I'd think the TGUs cover a lot of the same territory.
I eventually could do a press or two with the 40kg bell, which is the same weight I was doing my S&S TGUs with.