Since the Crack is an OTL amp there can be DC across the output for a bit as it starts up. That's why that resistor is across the output. It's a good idea to unplug your more delicate and expensive headphones before you turn the Crack on.
All the other amps have transformer outputs and thus won't have a DC offset across the output at startup but they could in theory thump when turned on.
The modded Quickie uses DHTs that heat up pretty much instantly and thus it might make a little noise, but since the headphone version is a DIY mod and not something we sell I don't have enough data to offer whether there is a turn on transient or not.
The stock S.E.X. kit uses indirectly heated tubes that take several seconds to warm up so there shouldn't be a thump unless maybe if you switched off a running amp and immediately switched it back on. If the kit has the C4S in it there might be a bit more chance of a thump as the tubes begin to conduct.
The Smack has a soft start and indirectly heated tubes. We were hot plugging power cords on our prototype yesterday, which doesn't even allow the soft start time to reset even so we had no problems whatsoever with thumps. And yes, once again that crazy accidental power cord kit of ours sounded better than some other aftermarket power cords.
All that said, better safe than sorry. If you are concerned, unplug your headphones before you turn on the amp.