You sure can move TS2009 to a portable drive. Once the data is moved, it's only a matter of recreating shortcuts of the Launcher and Content Manager, located in the bin folder.
There's some things to keep in mind though with portable drives. They are definitely slower than the internal drives due to their interface to the rest of the computer. Instead of being connected right to the motherboard, they use USB3.0, which is a bit slower. External drives also are similar to the drives used in laptops and tend to run at slower RPMs, which can affect performance a bit.
I'm saying this with experience, having done this myself when using TS12 on my laptop which doesn't quite have enough room to load up my TS12 install, and when running the install on someone else's computer.