Kind of, sort of. (You can't save as SVG, but you can export as PNG.) PS Touch projects themselves are self-contained UNTIL they are exported, and even then they'll get exported to a specific location. (e.g., To the Camera Roll or Gallery/Photos, to Creatve Cloud, etc.)
The procedure would be to start a new project using the "add image" icon (looks like a landscape with a plus sign, in the lower right in the project selection user interface) > Camera. Take your picture, then PS Touch will bring you to the editing user interface. Edit your image as appropriate.
Go back out to the project selection user interface by tapping the back arrow in the upper left to save. You can then export the project using the export icon (5th icon from the upper right).