Is it possible to use an SSD as a larger-capacity flash drive? I know that some computer cases include external SATA ports, so would it be reasonable to assume that one could interface with the SSD using a SATA cable?
While I assume you're referring to a solid state hard drive, I'll point out that most thumb drives use solid state technology as well. Performance is usually slower for thumbdrives as they use slower controllers, but you can find some that use the same SandForce controller used in most solid state hard drives.
The advantages of a real solid state hard drive over a non-SandForce thumbdrive would most likely be speed and price per GB.
Compared to a SandForce based thumb drive, the SSD would be bigger, heavier, and require an external enclosure or adapter.
I'd say if you're looking for speed and weight, go with a SandForce based thumbdrive, though you'll pay a premium for them.
Turns out that having an external SATA port is entirely unnecessary, as the free market has devised a solution for those who wish to use internal drives as portable drives: