It will run Final Cut Studio 2009, but Motion and Color may have some issues with the graphics card that's built in. But FCP will run just fine if you have the proper hard drive set up, and 8GB RAM (4 minimum).
You'll want a FW800 (not a FW400) hard drive like the Other World Computing "on-the-go" drive for your media (Scratch Disk) drive.
But it should be fine. The 13" screen is pretty small for editing with, but if that's all you can afford, it'll work.
Now, when it comes to capturing video from tape, there's going to be a problem. There's no ExpressCard slot on the 13" (only on the 17"), only one FW800, so you'll have to capture to your internal drive, then transfer it to the external drive, or hope you can capture successfully in small chunks to the external drive. See, the FW800 port will be strained if you have both the camera/deck and a hard drive attached to it at the same time (cam/deck plugged into the drive, drive plugged into the MPB).