Great question! The bottom line answer is that you can double-charge at any time using any press or any method. The only thing that changes is the specific mistake or malfunction that caused the double-charge. On a Lee Turret, eg, if you do not complete the ram's downward stroke for any reason (eg, interruption) it will not index and the next stroke will repeat the last . . . which could have been a powder drop.
Single stage or turret is often recommended for beginners because only one die is used at a time, for one round. You can see what's happening because there's nothing else to watch at that stroke/moment. You can do the same process on a single stage (eg crimping) many times in a row and get a feel for what change in stroke or adjustment does.
Starting single stage is also reasonable if you're doing rifle. You'll use that single stage press even if you eventually finish the cartridge on a progressive.
Starting progressive is very possible if you are attentive and retentive, and mechanically inclined to handle the adjustments that are often required to linkages, changeovers etc. Single stage avoids most of these issues so you can concentrate on making the cartridge.
I realized I wanted a progressive press for pistol when for the first time I did a batch of 300 rounds of 9mm, and it took 1500 strokes of a Lee Classic Turret and 300 hand-priming squeezes to complete. Would have been . . . er, will be nice to do that in 304 strokes lol.
In pistol, I'm also not at all concerned about slop in the turret or tool head making minor differences in the round, so progressive is fine. (I went with a Hornady LNL AP to minimize/eliminate those "issues" even for pistol). For rifle, for me, for now, it's a different story. Again, YMMV.
There are many ways to minimize the likelihood of double-charging, and what works for me may not work for you. Fortuitously, I use powders in both pistol (W231/HP38 in 380, 9mm, and 45ACP) and rifle that will overflow if doubled-up, or at least be visible near the top of the case.
But the BEST way (for me, YMMV) is to have room on my turret or progressive for a powder checker die that shows me the level of powder in each case. Double- and zero-charges are obvious, but it also shows minor variations in powder volume thrown.
If I were charging a batch of cartridges by hand, a flashlight examination of each or a wooden dowel (with a "fill line" drawn on it) dropped into each case is probably the best way to accomplish the same effect.