2 19VDC laptop chargers in series

[EricVanWyk]

I'm not comfortable with those blanket statements. We really don't know what is inside those converters.

Turning on one before the other applies a reversed polarity voltage across the slacker. That could become a problem. The classic and cheap transformer rectifier linear regulator setup has two components that possibly could have a problem. The output capacitor could be an electrolytic (as jason said) or a tantalum. A majority of linear regulators can't handle reversed polarity. As for switchers, depending on the topology the commutation cell could become an unintended reverse path and pop like the linear.

My comment about output filtering assumed a pair of identical supplies. Stacking switchers that operate at the same frequency isn't a good idea, as their control loops can become confused. The quick'n'dirty fix is to pi filter the accidental control connection away.