Now that shadowrun returns is available on both PC and mobile devices, can I transfer my save game from the PC over to, say, my android phone or vice versa?
Yes it's possible
As quoted from an admin on shadrowrun.com (here), follow those steps :
Step one: Connect your Android device to your computer, and ensure it's acting as a media device, (this lets you access it via USB to move files).
Step two: Grab the desired saved game(s) from your machine, (http://shadowrun-returns.wikispaces.com/Game+File+Locations+by+OS).
Step three: Copy the file(s) to Android/data/com.harebrainedschemes.shadowrun/files/Saves
Step four: Load Shadowrun Returns and verify the saved game files appear in "Load Game".
Step five: Play!
This is just an assumption but I think it might work the other way arround. However, I would backup files before overwritting anything. Better safe than sorry.