Maybe. For stuff like the personal notes you're keeping on a criminal conspiracy, a flash drive might be fine. But I'd be very skeptical of storing, say, the PHP source code to the Silk Road on a flash drive or SSD, because the internal data structures of the SSD could leak information about the sizes of individual files. If the feds can recover the sizes of individual files, rounded up to the next multiple of 4K, and you've got the PHP source code for the Silk Road stored there, it's game over. The same goes for filesystem encryption, like the kind ZFS (I think) has.

(I'm not personally familiar with ZFS, but the ZFS docs, especially https://docs.oracle.com/cd/E26502_01/html/E29007/gkkih.html#... really creep me with regard to this. The last thing you'd want is blocks in your local encrypted copy of PHP source code to be compressed first. And so then you'd think you'd want encryption enabled on a pool, but from reading the docs it seems that feature merely makes the filesystems on that pool inherit that encryption option, instead of doing some sort of filesystem-blind block-level encryption, where there's any variance in the encryption of blocks, or any information that could be derived from locations of blocks. So I think the suggestion to encrypt on a directory-by-directory basis to limit your exposure is not a very good one. I'd recommend that you use a spinning hard drive, whole disk encryption of the sort we have today, take out the battery, and keep your foot by the power outlet.)

If the laptop turned off and the drive was encrypted by what basic method could they extrapolate the same information as if the computer was decrypted and powered on? Are you referring to some kind of memory attack? Wouldn't they need to be prepared to do that kind of forensic work in the extremely near term (or have some equipment on-hand to preserve the memory at least)? I'm pretty uninformed in this area and would appreciate a lesson.

The idea is that typically people expect a laptop to remain powered when the cord is unplugged (due to the battery), and so in a situation where the laptop is grabbed the power is cut immediately (and unexpectedly) and the hard-drive is no longer decrypted. As another commenter pointed out, a forensics team could then probably grab whatever they needed from the system memory (presuming they acted fast enough), but as I understand it the problem becomes significantly more complicated.

Well, if you want to be ready to quick-twitch turn off the device, pulling a power cord is usually a lot simpler than removing the battery.