I think both options are good. Both pat and draw one has merit.

If we draw 1->pat, then our average badugi range will be much stronger. The con is that we will have some rough 1card draw that we decide to 3bet and snow (like 765)

If we pat from the beggining it's good because usually when somebody is pat from the start and bet the river they don't have any bluffs. But if we have these, 4 low same suited hand we can balance this out. The con is that our average badugi range is much weaker (we will have a lof of Q/K), and some aggro opponent can/will attack that range and put a lot of pressure to us.

I think it mostly depends about the opponent. How he plays. How he thinks about certain spots whether i play as a 1c draw or pat these hands.

And yes, i will definately 3bet and snow with A256 SB vs BTN. You can also 3bet/snow BTN vs HJ, you will not oversnow if you have these hands in your range. However if you also 3bet some rougher 3card draws, with the plan to snow (like 765, 762, etc), and play all of your range 1->pat and try to represent a badugi, you will oversnow.

But it should depend on the opponent, against some players we can get away by this. Again some players who bluff (snow) catch very light we should reduce this freq. close to 0, etc...