I wouldn't want to find out the hard way. I have a BMD decklink 4k mini monitor PCIe card. I used to use it in a PC, but I upgraded to a laptop. To replace with an external input device is too expensive unless I downgrade capability significantly.
PCIe chassis are more expensive than expected but I've noticed ones that specifically call themselves 'eGPU enclosures'. For some reason when they're marketed to that specific purpose, they cost a lot less, probably because they often don't come with power supplies (which I actually have spare).
I'm looking at 2 such eGPU enclosures and they are a decent price and I think they should work, but I'm a little scared by them specifically saying "eGPU". Would I likely have any problems buying one of those for my PCIe device rather than for a graphics card? Or is PCIe, PCIe regardless?
With thunderbolt you can connect it whenever you please. Your OS doesn't initiate the thunderbolt connection until it's in the operating system anyways. Plug it in, turn it on it makes no difference. Disconnecting you need to make sure you safely eject the device or you will get a blue screen.
M.2 adapters are almost never hot plugable, those need to be done with your laptop off. That is literally the same as having a desktop and slotting in the card there. Just make sure your enclosure is off when you're connecting or disconnecting anything and you won't hurt anything.
I think the trouble is this decklink device is not ejectable. It's not storage. I can always be sure to power down the laptop before disconnect the enclosure perhaps.